Parameters

In this appendix we list all the different parameters that can be specified when carrying out a simulation. Most of these parameters must be specified in program units, defined by the field and spacetime transformations of Eq. (2), so that variables are dimensionless. For example, one must introduce the length side of the box as \(\tilde{L} \equiv L \omega_*\), the infrared cutoff of the lattice as \(\tilde{k}_{\rm IR} \equiv k_{\rm IR}/\omega_*\), etc.

The tables below are generated automatically from the parameter database source/data/parameters.yaml by scripts/gen_param_appendix.py. Only the content between the @gen:params / @endgen HTML-comment markers is generated; the surrounding text is authored by hand. The Type column annotates vector-valued parameters with their arity (e.g. ×2 for a fixed length, or a symbolic count such as ×NS for the number of scalar fields); a — default means the parameter is optional with no default, while required marks a mandatory parameter.

Run parameters

These parameters control the lattice, the time evolution and the background expansion. They are declared in include/CosmoInterface/runparameters.h.

Parameter	Type	Default	Units	Description
N	int	required	dimensionless	Number of lattice points per spatial dimension (the lattice is N^3 in 3D).
kIR	float	-1	program units	Infrared cutoff of the lattice in program units; the minimum (nonzero) momentum on the lattice.
lSide	float	-1	program units	Comoving side length of the cubic simulation box in program units.
dx	float	-1	program units	Comoving lattice spacing in program units.
dt	float	required	program units	Time step of the evolution algorithm in program units.
expansion	bool	true	dimensionless	If true, the scale factor evolves self-consistently via the Friedmann equations; if false, the scale factor is fixed to unity and dynamics occur in Minkowski spacetime.
t0	float	0	program units	Initial time of the simulation in program units.
tMax	float	10000*dt	program units	Final time of the simulation in program units.
fixedBackground	bool	false	dimensionless	If true, replaces the self-consistent expansion by a fixed background expansion specified through omegaEoS and H0.
omegaEoS	float	1/3	dimensionless	Barotropic equation-of-state parameter w = p/rho used for the fixed background expansion (e.g. 0.333 for radiation domination).
H0	float	required	GeV	Initial Hubble rate used for the fixed background expansion (in GeV).
a0	float	1.0	dimensionless	Initial value of the scale factor at the start of the simulation.
evolver	enum	LF	n/a	Type of time-evolution algorithm: LF (staggered leapfrog), velocity-Verlet (VV), position-Verlet (PV), or Runge-Kutta (RK*) schemes of various orders. Allowed values: LF, VV2, VV4, VV6, VV8, VV10, VV6_2, RK2, RK3_3, RK3_4, RK4_5, PV2, PV4, PV6, PV8, PV10, PV6_2.
tolerance	float	-1	dimensionless	Error tolerance used by adaptive (e.g. Runge-Kutta) solvers to control the adaptive time step.
doDiffusion	bool	false	dimensionless	Master switch enabling a post-evolution diffusion phase, in which the fields are further relaxed after the main simulation has finished (used e.g. to smooth defect configurations). The diffusion-phase parameters (tmaxdiff, dtdiff, diffusionevolver, tOutputFreqDiff, tOutputRareFreqDiff, snapshots_diffusion) are only read when this is true.
tmaxdiff	float	—	program units	Duration (maximum time) of the diffusion phase in program units.
dtdiff	float	—	program units	Time step used during the diffusion phase in program units.
diffusionevolver	enum	RK2	n/a	Time-evolution algorithm used during the diffusion phase (same set of integrators as evolver). Allowed values: LF, VV2, VV4, VV6, VV8, VV10, VV6_2, RK2, RK3_3, RK3_4, RK4_5, PV2, PV4, PV6, PV8, PV10, PV6_2.
doResolutionPreserving	bool	false	dimensionless	Master switch enabling the resolution-preserving technique, which rescales the lattice and fields during the run to keep the relevant physical scales resolved. Its parameters (sRP, tRP0, tRPMax) are only read when this is true.
sRP	float	—	dimensionless	Rescaling (stretch) factor applied by the resolution-preserving technique.
tRP0	float	t0	program units	Time at which the resolution-preserving rescaling starts, in program units.
tRPMax	float	(computed)	program units	Time at which the resolution-preserving rescaling stops, in program units.

Note

\(\tilde{k}_{\rm IR}\) and \(\tilde{L}\) obey \(\tilde{k}_{\rm IR} = 2\pi /\tilde L\), so only one of them must be specified for the simulation: the other one will be automatically computed by the code.

Initial conditions

These parameters control the initial field fluctuations and the random seed. They are declared in include/CosmoInterface/runparameters.h.

Parameter	Type	Default	Units	Description
kCutOff	float	-1	program units	Momentum cutoff imposed in the spectrum of initial scalar fluctuations: modes above this momentum are set to zero. A value of -1 (default) means no cutoff (internally set to 2*kUV); 0 means initially vanishing fluctuations.
ICtype_S	enum	Default	n/a	Type of initial conditions used for scalar singlet fields (e.g. default vacuum fluctuations, random-with-matter, defect networks, white-noise defects, or homogeneous). Allowed values: Default, RandomWithMatter, DefectsNetwork, DefectsWhiteNoise, Homogeneous.
ICtype_U1	enum	Default	n/a	Type of initial conditions used for U(1) gauge fields (e.g. default, random-with-matter, plane waves, plane waves with zero magnetic field, Bunch-Davies transverse modes, or defect networks). Allowed values: Default, RandomWithMatter, PlaneWaves, PlaneWavesZeroB, BunchDavisTransverseU1, DefectsNetwork, DefectsWhiteNoise.
baseSeed	string	required	n/a	Seed for the random generator of initial field fluctuations; if not specified, a seed is generated randomly each run.
lcorr	float	—	program units	Initial comoving correlation length of the defect network used when generating DefectsNetwork initial conditions.
deltaNoise	float	—	dimensionless	Amplitude of the white-noise field distribution used when generating DefectsWhiteNoise initial conditions.
ext_PS	string ×NS	defaultString	path	Per-scalar external initial power spectrum: path/name of a file providing the initial spectrum used to set the initial conditions of scalar singlet field i.

Note

Typically, you will also need to add some parameters to get the initial homogeneous components of your fields in the user-defined model file, see Section My first model of (singlet) scalar fields for more details.

Output parameters

These parameters control how, how often and in which format the simulation output is written.

Parameter	Type	Default	Units	Description
tOutputFreq	float	10*dt	program units	Time interval between the printing of frequent output (e.g. averages) in program units.
tOutputInfreq	float	100*dt	program units	Time interval between the printing of infrequent output (e.g. spectra) in program units.
tOutputRareFreq	float	1000*dt	program units	Time interval between the printing of very infrequent (rare) output in program units.
tOutputVerb	float	100*dt	program units	Time interval between progress updates printed to the terminal in program units.
outputfile	string	./	path	Folder where simulation output is saved; defaults to the current/compilation folder.
hdf5Averages	bool	false	dimensionless	If true, averaged output quantities are written in HDF5 format instead of text format.
hdf5FlushFreq	int	10	dimensionless	Number of writes between flushes of buffered HDF5 output to disk.
hdf5Spectra	bool	false	dimensionless	If true, field spectra are printed in HDF5 format; if false, they are printed in text format.
appendToFiles	bool	false	dimensionless	If true, output is appended to pre-existing files; if false, existing files cause an error unless overwriteFiles=true.
overwriteFiles	bool	false	dimensionless	If true (and appendToFiles=false), existing output files are deleted before writing.
print_headers	bool	false	dimensionless	If true, a header line describing the contents is printed at the top of each text output file.
fn_verbosity	int	0	dimensionless	Verbosity level controlling how much model/parameter information is embedded in output filenames (0 = none; higher levels append N, kIR, dt, evolver, etc.).
tOutputFreqDiff	float	10*dtdiff	program units	Time interval between frequent output during the diffusion phase, in program units (the diffusion-phase counterpart of tOutputFreq).
tOutputRareFreqDiff	float	100*dtdiff	program units	Time interval between rare/infrequent output during the diffusion phase, in program units (the diffusion-phase counterpart of tOutputRareFreq).
measureDefectsEnergies	bool	false	dimensionless	If true, enables measurement and output of the energy stored in the defect network.
measureDefectsStructure	bool	false	dimensionless	If true, enables measurement and output of the defect-network structure/geometry (e.g. defect positions and length/area).

Spectra parameters

These parameters control the binning and the estimators used when computing the field power spectra.

Parameter	Type	Default	Units	Description
spectraVerbosity	int	0	dimensionless	Verbosity level controlling how much additional information is written into the spectra files.
deltaKBin	float	1	dimensionless	Width of the momentum bins used in the field spectra; the number of bins is approximately sqrt(3)N/(2deltaKBin).
PS_type	int	1	dimensionless	Power spectrum type selector controlling the binning/estimator used for the power spectra.
PS_version	int	1	dimensionless	Power spectrum version selector choosing among different power spectrum implementations.
flagON	bool	false	dimensionless	If true, enables the O(N) power spectrum computation/output for O(N) scalar field models.
flagChiralPS	bool	false	dimensionless	If true, enables computation/output of chiral (helicity-decomposed) power spectra.
saveUnbinnedSpectra	bool	false	dimensionless	If true, the unbinned (per-mode) power spectra are saved in addition to the binned spectra.

Snapshot parameters

These parameters select which energy contributions are saved as field snapshots (in HDF5 format) and over which sub-volume of the lattice.

Parameter	Type	Default	Units	Description
snapshots	string ×14	(empty list — no snapshots saved)	n/a	Space-separated list of the configuration-space quantities to dump as HDF5 field snapshots. Each entry must be one of the 14 recognised labels; you list any subset (in any order), one label per quantity you want saved. Recognised labels: S (scalar-singlet field value), E_S_K / E_S_G (scalar-singlet kinetic / gradient energy), CS (complex-scalar modulus), E_CS_K / E_CS_G (complex-scalar kinetic / gradient energy), E_SU2D_K / E_SU2D_G (SU(2)-doublet kinetic / gradient energy), E_A_K / E_A_G (U(1) electric / magnetic energy), E_B_K / E_B_G (SU(2) electric / magnetic energy), E_V (potential energy), E (total energy). Selecting a label for a sector the model does not contain is harmless and simply produces no file.
energy_snapshot	string ×14	—	n/a	Deprecated alias for snapshots, kept for backward compatibility. If snapshots is not given but energy_snapshot is, its value fills snapshots and a deprecation notice is printed. If both are given, snapshots takes precedence and a conflict warning is printed.
snap_lowercoord	int ×NDim	{0,...} (one 0 per dimension)	dimensionless	Lower corner (in lattice units) of the sub-volume saved in snapshots, one value per spatial dimension. Together with snap_uppercoord and snap_stepcoord it selects which lattice region is written: snap_lowercoord is the first lattice index kept along each axis. Default 0 in every dimension (start at the box edge).
snap_uppercoord	int ×NDim	{N,...} (one N per dimension)	dimensionless	Upper corner (in lattice units) of the sub-volume saved in snapshots, one value per spatial dimension. snap_uppercoord is the (exclusive) last lattice index kept along each axis. Default N (the lattice size) in every dimension, i.e. the full box.
snap_stepcoord	int ×NDim	{1,...} (one 1 per dimension)	dimensionless	Stride (in lattice units) used when sampling the snapshot sub-volume, one value per spatial dimension. A value of s keeps every s-th lattice point along that axis (coarsening the saved data); 1 means keep every point.
snapshots_diffusion	string ×15	(empty list — no snapshots saved)	n/a	Space-separated list of the configuration-space quantities to dump as HDF5 field snapshots during the diffusion phase (the diffusion-phase counterpart of snapshots). Same recognised labels as snapshots; you list any subset (in any order), one label per quantity you want saved.

Gravitational waves

These parameters control the evolution of the tensor perturbations used to compute the gravitational-wave spectrum.

Parameter	Type	Default	Units	Description
withGWs	bool	false	dimensionless	If true, the simulation evolves the tensor perturbations to compute the gravitational wave spectrum (allocates the GW field tensor and its conjugate momentum, fldGWs and piGWs).
doLFforGWs	bool	true	dimensionless	If true, the gravitational wave (tensor) sector is evolved with the leapfrog (LF) evolver; if false, it uses the same evolver as the fields.
GWprojectorType	int	2	dimensionless	Type of transverse-traceless projector used for the gravitational waves (1 = real, 2 = backwards/default, 3 = forward).

Saving and restarting

These parameters control end-of-run saving, periodic backups and restarting from a previously saved simulation.

Parameter	Type	Default	Units	Description
tBackupFreq	float	-1	program units	Time interval between backups of the simulation state in program units; a negative value disables backups.
save_dir	string	defaultString	path	Folder where a copy of the simulation is saved at the end of the run, which can be loaded as the starting point of a new simulation.
backup_dir	string	defaultString	path	Folder where a copy of the simulation is saved at backup times during the run.
load_file	string	defaultString	path	Full path/name of an HDF5 file from which to restart (load) a previously saved simulation; if provided the simulation runs in restart mode and the parameter parser is switched to override mode so new parameters can supersede the saved ones.
load_dir	string	defaultString	path	Backward-compatibility alias for 'load_file' (named to match a typo in the first manual); supplies the restart file name when 'load_file' is not given. The full file name is still required.

Gauge couplings and charges

These framework-level coupling parameters set the gauge couplings and charges of the gauge sectors, as well as a few related per-field couplings. They are declared in the constructor of include/CosmoInterface/abstractmodel.h and in the corresponding gauge-field interface headers.

Parameter	Type	Default	Units	Description
gU1s	float ×#U1	1.0	dimensionless	Gauge couplings of the U(1) gauge fields, one per U(1) field; combined with per-couple charges to set the effective charges of complex scalars and SU(2) doublets coupled to U(1).
CSU1_charges	float ×#couples	1	dimensionless	Charges of each complex-scalar / U(1)-gauge-field coupled pair; combined with gU1s to form the effective charges of the complex scalars under their U(1) gauge fields.
SU2DoubletU1_charges	float ×#couples	1	dimensionless	Charges of each SU(2)-doublet / U(1)-gauge-field coupled pair; combined with gU1s to form the effective charges of the SU(2) doublets under their U(1) gauge fields.
gSU2s	float ×#SU2	1.0	dimensionless	Gauge couplings of the SU(2) gauge fields, one per SU(2) field; combined with per-couple charges to set the effective charges of SU(2) doublets coupled to SU(2).
SU2DoubletSU2_charges	float ×#couples	1	dimensionless	Charges of each SU(2)-doublet / SU(2)-gauge-field coupled pair; combined with gSU2s to form the effective charges of the SU(2) doublets under their SU(2) gauge fields.
tNonLinearAxionU1	float	-1	program units	Program time at which to switch from linear to non-linear evolution for the axion-U(1) (Chern-Simons) coupling; a default of -1 disables the switch (coupling treated normally / non-linear feature off).
gAxionU1	float ×#couples	1.0	dimensionless	Gauge coupling(s) for the axion / U(1) gauge field (Chern-Simons) interaction, one per axion-U(1) gauge entry; combined with alphaLambda_AxionU1 to set the effective axion-U(1) couplings.
alphaLambda_AxionU1	float ×#couples	1	dimensionless	Dimensionless axion-U(1) Chern-Simons coupling strength (alpha/Lambda) for each axion / U(1)-gauge-field coupled pair; combined with gAxionU1 to set the effective axion-U(1) charges.
xis	float ×#NMC	1	dimensionless	Non-minimal gravitational coupling constants xi for each non-minimally-coupled scalar field, entering the xiRphi^2 term in the action.

Model-specific parameters

In addition to the framework parameters above, each shipped model declares its own parameters (couplings, masses, and the initial homogeneous amplitudes and momenta of its fields). The tables below list these per model, using the model name as it is passed to the compilation. Vector-valued initial conditions are annotated with their arity (e.g. ×NS for the number of scalar fields).

lphi4

Parameter	Type	Default	Units	Description
lambda	float	required	dimensionless	Quartic self-coupling of the inflaton field, appearing in the inflaton potential term 0.25lambdaphi^4; together with q it sets the resonance coupling g=sqrt(qlambda) and the field/time rescalings (omegaStar=sqrt(lambda)fStar).
q	float	required	dimensionless	Resonance parameter controlling the strength of the interaction term 0.5q(phichi)^2 between the inflaton and the daughter field; the derived coupling g is defined as sqrt(qlambda).
initial_amplitudes	float ×2	required	GeV	Initial homogeneous amplitudes of the two scalar fields (inflaton and daughter field), given in GeV; the first component (inflaton) also sets the field rescaling fStar=fldS0[0].
initial_momenta	float ×2	{0,0}	GeV^2	Initial homogeneous time-derivatives (canonical momenta) of the two scalar fields, given in GeV^2; optional parameter defaulting to zero velocity for both fields.

defects_ONGlobal

Parameter	Type	Default	Units	Description
lambda	float	1.	dimensionless	Quartic self-coupling of the real O(N) scalar multiplet whose spontaneous symmetry breaking produces the global defects (domain walls for N=1, global strings for N=2, monopoles/textures for higher N); it sets the velocity rescaling omegaStar=sqrt(lambda)*vev and enters the derived bias coupling g=qbias/lambda.
vev	float	1.	GeV	Vacuum expectation value of the O(N) scalar multiplet, i.e. the radius of the vacuum manifold on which the defect network forms; it sets the field rescaling fStar=vev and the velocity rescaling omegaStar=sqrt(lambda)*vev.
qbias	float	0.	dimensionless	Bias parameter adding a term that breaks the vacuum degeneracy, used to bias domain-wall networks; it sets the derived bias coupling g=qbias/lambda. A value of 0 gives an unbiased network.

defects_U1LocalStrings

Parameter	Type	Default	Units	Description
lambda	float	1.	dimensionless	Quartic self-coupling of the complex scalar field, controlling the strength of the symmetry-breaking potential whose vacuum manifold supports the formation of local cosmic strings; together with the vacuum expectation value vev it sets the velocity rescaling omegaStar = sqrt(lambda)*vev.
vev	float	1.	GeV	Vacuum expectation value of the complex scalar field, i.e. the radius of the vacuum manifold on which the local cosmic strings form; it sets the field rescaling fStar=vev and the velocity rescaling omegaStar=sqrt(lambda)*vev.

NMC_lphi4

Parameter	Type	Default	Units	Description
lambda	float	required	dimensionless	Quartic self-coupling of the inflaton (first scalar) in the lphi4 potential 0.25lambdaphi^4; sets the characteristic frequency omegaStar=sqrt(lambda)fStar and, together with q, the derived coupling g=sqrt(qlambda).
initial_amplitudes	float ×2	required	program units	Initial homogeneous amplitudes of the two scalar fields (in program/reduced-Planck units); the first entry fixes fStar=initial_amplitudes[0] used to define omegaStar=sqrt(lambda)*fStar.
initial_momenta	float ×2	{0,0}	program units	Initial homogeneous time-derivatives (conjugate momenta) of the two scalar fields; defaults to zero velocity for both fields if not specified.

lphi4SU2U1

Parameter	Type	Default	Units	Description
initial_amplitudes	float ×NS	required	GeV	Initial homogeneous amplitude of the real scalar singlet field (fldS0). Read as get for the single scalar singlet (NScalars=1).
initial_momenta	float ×NS	required	GeV^2	Initial homogeneous time-derivative (conjugate momentum) of the real scalar singlet field (piS0). Read as get for the single scalar singlet (NScalars=1).
cmplx_field_initial_norm	float	required	GeV	Initial homogeneous norm of the complex scalar field; the norm is distributed equally between the two real components via Complexify(norm/sqrt(2), norm/sqrt(2)) to set fldCS0(0_c).
cmplx_momentum_initial_norm	float	required	GeV^2	Initial homogeneous norm of the complex scalar field momentum (time derivative); distributed equally between the two real components via Complexify(norm/sqrt(2), norm/sqrt(2)) to set piCS0(0_c).
SU2Doublet_initial_norm	float	required	GeV	Initial homogeneous norm of the SU(2) doublet field (in GeV); distributed equally between the four real components via MakeSU2Doublet(a, norm/2) to set fldSU2Doublet0(0_c). Also sets the field rescaling fStar and (with lambda) the frequency rescaling omegaStar = sqrt(lambda)*norm.
SU2Doublet_initial_momenta_norm	float	required	GeV^2	Initial homogeneous norm of the SU(2) doublet field momentum (time derivative, in GeV^2); distributed equally between the four real components via MakeSU2Doublet(a, norm/2) to set piSU2Doublet0(0_c).
qG	float	required	dimensionless	Dimensionless coupling ratio controlling the interaction between the SU(2) doublet and the real scalar singlet; enters the potential term qG(|H|S)^2 and fixes the effective coupling g = sqrt(qG*lambda) (derived).
qH	float	required	dimensionless	Dimensionless coupling ratio controlling the interaction between the SU(2) doublet and the complex scalar; enters the potential term 2qH(|H||phi|)^2 and fixes the effective coupling h = sqrt(qHlambda) (derived).
lambda	float	required	dimensionless	Quartic self-coupling of the SU(2) doublet (potential term |H|^4); also sets the frequency rescaling omegaStar = sqrt(lambda)SU2Doublet_initial_norm and the derived couplings g = sqrt(qGlambda), h = sqrt(qH*lambda).

lphi4U1

Parameter	Type	Default	Units	Description
cmplx_field_initial_norm	float	required	GeV	Initial homogeneous amplitude (norm) of the complex scalar field; it is distributed equally between the two real components via Complexify and also sets the field rescaling fStar used to define program units.
cmplx_momentum_initial_norm	float	required	GeV^2	Initial homogeneous amplitude (norm) of the complex scalar field's conjugate momentum (time derivative), distributed equally between the two real components via Complexify.
lambda	float	required	dimensionless	Quartic self-coupling of the complex scalar in the V = lambda|phi|^4 potential; it sets the velocity rescaling omegaStar = sqrt(lambda)cmplx_field_initial_norm and, together with the gauge charge, the derived gauge coupling g = sqrt(q*lambda).

axionU1_m2phi2

Parameter	Type	Default	Units	Description
initial_amplitudes	float	required	GeV	Initial homogeneous amplitude of the single real (axion) scalar field; its first component sets the field rescaling fStar used to convert to program units.
initial_momenta	float	required	GeV^2	Initial homogeneous velocity (conjugate momentum) of the single real (axion) scalar field.
Mass	float	required	GeV	Mass of the scalar field in the quadratic potential V = (1/2) m^2 phi^2; sets the velocity rescaling omegaStar = mass used to convert to program units.

NMC_tanh4_w_mass_P

Parameter	Type	Default	Units	Description
Hstar	float	required	GeV	Hubble rate 14 efolds before the end of inflation (begin of linear analysis), in GeV; also used as the velocity rescaling omegaStar to go to program units.
V0	float	required	dimensionless	Dimensionless amplitude of the inflaton tanh^4 potential, equal to Lambda4/(4 * mp^2 * Hstar^2).
M	float	required	dimensionless	Characteristic field scale M of the inflaton tanh(phi/M)^4 potential, expressed in units of the reduced Planck mass mp.
lambdaNMC	float	required	dimensionless	Quartic self-coupling of the non-minimally coupled (NMC) second scalar field.
mNMC	float	required	dimensionless	Mass of the non-minimally coupled (NMC) second scalar field, in units of Hstar (it enters the program potential as 0.5mNMC^2phi^2).
initial_amplitudes	float ×2	required	GeV	Initial homogeneous field amplitudes for the two scalar fields (inflaton and NMC field), in GeV.
initial_momenta	float ×2	{0, 0}	GeV^2	Initial homogeneous field velocities (conjugate momenta) for the two scalar fields, in GeV^2; optional, defaults to zero for both fields.

tanh2

Parameter	Type	Default	Units	Description
M	float	required	GeV	Mass scale appearing in the tanh^2 inflaton potential V = (M^2/2) tanh^2(phi/M); together with Lambda4 it sets the inflaton oscillation frequency omega = sqrt(Lambda4/M^2). Default in example input is 2.435e19 GeV (the reduced Planck mass).
Lambda4	float	required	GeV^2	Energy-scale-squared parameter of the tanh^2 inflaton potential; combined with M it fixes the inflaton oscillation frequency omega = sqrt(Lambda4/M^2), which is used as the velocity rescaling omegaStar. Example value 1.7966e65 GeV^2.
q	float	required	dimensionless	Resonance parameter setting the strength of the quartic interaction (q/2) phi^2 chi^2 between the inflaton and the daughter field; determines the effective coupling g = sqrt(q)*omega/phii. Example value 4e4.
initial_amplitudes	float ×2	required	GeV	Initial homogeneous amplitudes of the two scalar fields (inflaton, daughter) in GeV; the first entry phii = fldS0[0] sets the field rescaling fStar. Example: 3.39928e18 0.
initial_momenta	float ×2	{0,0}	GeV^2	Initial homogeneous velocities (conjugate momenta) of the two scalar fields in GeV^2; defaults to zero for both fields if not specified. Example: -3.0714e31 0.