arXiv subjects

Sarunas Verner

Publications and source records attributed to Sarunas Verner.

At least 19 recordsLinked to original sources

arXiv2026

Axion isocurvature and the model-building problem of low-scale inflation

The pre-inflationary QCD axion is often said to require low-scale inflation. We derive a general isocurvature bound for a light axion with a scale-invariant spectrum, treating its inflationary normalization $f_I$ independently of the late-time decay constant $f_a$ and allowing for an arbitrary axion dark matter fraction, nontrivial perturbation transfer, and the full anharmonic abundance response. In the minimal benchmark, where axions constitute all of the dark matter, $f_I=f_a\leq M_{\rm Pl}$, and the angular perturbation is conserved, the least restrictive CMB limit considered gives the 95% C.L. upper bound $H_I<1.25\times10^{10}\,\mathrm{GeV}$ on the inflationary Hubble scale. For an initial misalignment angle $\theta_i=1$, the bound strengthens to $H_I<2.2\times10^7\,\mathrm{GeV}$, with still stronger constraints near the hilltop. Combining the isocurvature and tensor spectra yields axion-tensor and axion-conditioned Lyth bounds. If the observed curvature perturbation is generated by a canonical cold single-field slow-roll inflaton and the tensor amplitude varies slowly across the observable CMB window, these relations limit the inflaton excursion to $\Delta\phi_{\rm CMB}/M_{\rm Pl}\lesssim10^{-7}\text{-}10^{-4}$ and require $|M_{\rm Pl}V'/V|\sim10^{-8}\text{-}10^{-5}$ while $M_{\rm Pl}^2V''/V\sim-10^{-2}$. This hierarchy favors models with independent control of the inflationary scale, potential derivatives, exit, and reheating, including hybrid, running-mass, and inflection-point models. Reheating and the requirement of Peccei-Quinn non-restoration sharpen these conditions, while nonminimal scenarios can relax them by modifying the primordial fluctuation, its transfer, or the relic abundance.

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arXiv2026

Reheating in No-Scale Models of Inflation

Analogously to the suppression of inflaton decays into conformally-coupled scalar fields in the original Starobinsky $R + R^2$ model of inflation, inflaton decays to Standard Model fields are also suppressed in minimal no-scale models of inflation with field space curvature $\mathcal{R} = 2/3$. We study how this suppression can be avoided in generalized no-scale inflationary models. These include models in which the field space curvature $\mathcal{R} = 2/(3\alpha)$ with $\alpha \ne 1$ as exemplified by models derived from string theory, as well as models with non-minimal gauge kinetic terms and anomaly-induced couplings. We analyze direct and anomaly-induced inflaton couplings to gauge bosons and gauginos and demonstrate the K\"ahler-frame invariance of the physical gauge coupling. We determine the resulting reheating temperatures and the corresponding predictions in the $(n_s,r)$ plane. Finally, we consider an $R^3$ deformation of Starobinsky supergravity, which modifies the inflaton and stabilizer sectors but does not, by itself, generate new tree-level inflaton couplings to visible matter fields.

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arXiv2026

Cosmological gravitational particle production in multifield inflation

We study cosmological gravitational particle production (CGPP) of dark matter in two-field inflationary backgrounds with both flat and curved field-space geometries. As a concrete realization of broader multifield mechanisms, we adopt a Starobinsky+quadratic potential and construct benchmark scenarios that interpolate between the flat field-space limit and the sidetracked attractor on a hyperbolic field space, and we compute the production spectrum of a gravitationally coupled spectator scalar for both minimal ($\xi = 0$) and conformal ($\xi = 1/6$) coupling to the Ricci scalar. We show that negative field-space curvature can strongly enhance the post-inflationary oscillations of the Ricci scalar, leading to an enhancement of up to an order of magnitude in the CGPP number density relative to the flat field-space limit, particularly for minimal coupling. For the sidetracked attractor, this enhanced production competes with a reduced inflationary energy scale, leading to a nontrivial dependence of the relic abundance on model parameters. We derive the relic abundance as a function of spectator mass and reheating temperature, and identify the viable parameter space for each benchmark. The conformal case $\xi = 1/6$, whose scalar mode equation is structurally analogous to that of a massive Dirac fermion, is much less constrained by isocurvature and provides a minimal scenario for purely gravitational dark matter production in multifield inflation.

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arXiv2026

Gravitational Waves from Matter Perturbations of Spectator Scalar Fields

We compute the stochastic gravitational wave background sourced at second order by a spectator scalar field $\chi$ coupled to the inflaton $\phi$ through a portal interaction $\sigma\phi^2\chi^2$ and with quartic self-interaction $\lambda_\chi\chi^4/4!$. In the large portal coupling regime ($\sigma/\lambda \gg 1$, with $\lambda$ the inflaton normalization), parametric resonance during reheating amplifies the spectator power spectrum by many orders of magnitude near the resonance band until Hartree backreaction from the quartic coupling detunes the instability, while the large inflationary effective mass suppresses superhorizon power and ensures compatibility with CMB isocurvature bounds. We focus on the direct field-gradient source $\partial_a\chi\,\partial_b\chi$ in the second-order Einstein equations and derive a master formula that factorizes into a spectral integral over the frozen, vacuum-subtracted spectator spectrum and a time integral encoding the post-inflationary expansion history. For our benchmark reheating history we obtain analytic scaling relations, including a peak amplitude $\Omega_{\rm GW}\propto T_{\rm reh}^{8/3}$, strong dependence on the portal strength, and weak sensitivity to $m_\chi$. We validate the framework against nonlinear lattice simulations, demonstrating complementarity: the Hartree treatment captures superhorizon evolution inaccessible to the lattice, while the lattice resolves rescattering and fragmentation near the spectral peak. For $\sigma/\lambda \simeq 10^4$ and $T_{\rm reh}=2 \times 10^{14}\,\mathrm{GeV}$, the signal reaches $\Omega_{\rm GW}h^2\sim 10^{-11}$ at $f\sim10^{7}$-$10^{8}\,\mathrm{Hz}$. Increasing $\lambda_\chi$ at fixed $\sigma$ has a non-monotonic effect: small values enhance the signal via rescattering, whereas larger values suppress it by detuning the resonance.

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arXiv2025

Gravitational Production of Massive Spin-2 Particles During Reheating

We study the minimal gravitational portal for a massive spin-2 dark matter candidate $X_{\mu\nu}$ produced during perturbative reheating. The dark sector couples to the visible sector only via gravity, and we analyze two unavoidable channels: (i) inflaton condensate annihilation, $\phi+\phi \to X+X$, and (ii) thermal scatterings, ${\rm SM}+{\rm SM}\to X+X$, both mediated by graviton exchange. Working in the Fierz-Pauli framework for a free massive spin-2 field of mass $m_2$, we derive the graviton-mediated amplitudes and perform a full helicity decomposition of the final state. The relic abundance is obtained analytically in terms of $m_2$ and the reheating temperature $T_{\rm RH}$. In the light mass regime $m_2 \ll m_\phi$ (with $m_\phi$ the inflaton mass during oscillations), production is overwhelmingly dominated by the longitudinal (helicity-0) mode: the $2\to2$ cross section is parametrically enhanced, scaling as $\sim (m_\phi/m_2)^4$, and yields efficient dark matter production despite purely gravitational couplings. Compared to lower-spin cases (spin-$0$, $1/2$, $1$, and $3/2$), massive spin-$2$ production is substantially more efficient for the same reheating history. Over most of the parameter space the inflaton condensate channel dominates the yield, while the thermal contribution is negligible. Avoiding overproduction typically requires either a relatively low $T_{\rm RH}$ or a spin-$2$ mass near threshold, $m_2 \lesssim m_\phi$. This places the spin-$2$ portal on similar footing to other higher spins in reheating scenarios, while emphasizing the central role of the helicity-$0$ mode and the reheating history in setting the dark matter density.

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arXiv2025

Gravitational Waves from Isocurvature Perturbations of Spectator Scalar Fields

We present a mechanism for gravitational wave (GW) production from isocurvature perturbations in spectator scalar fields during inflation. These energetically subdominant fields develop blue-tilted power spectra through inflationary dynamics, generating second-order scalar perturbations that source a stochastic GW background. The mechanism naturally satisfies CMB constraints at large scales while producing enhanced signals at smaller scales across a broad frequency range $10^{-20} - 1$ Hz. We perform comprehensive numerical and analytical calculations of the complete isocurvature spectrum evolution, including gravitational particle production, reheating dynamics, and scalar-induced GW generation. For spectator fields with effective masses $0.5 \lesssim m_{\chi,\mathrm{eff}}/H_I$, the resulting GW energy density reaches $\Omega_{\text{GW}} h^2 \sim 10^{-20}$-$10^{-12}$, accessible to pulsar timing arrays, space-based interferometers, and next-generation CMB experiments. Our analysis reveals that GW-induced constraints exceed current isocurvature bounds. We examine both unstable (curvaton-like) and stable (dark matter) spectator fields, demonstrating strong sensitivity to reheating temperature, inflaton-spectator coupling, and decay dynamics. This framework establishes isocurvature-sourced GWs as a powerful probe of early universe physics, enabling simultaneous constraints on inflationary dynamics, dark matter production, and reheating through coordinated multi-frequency GW observations.

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arXiv2025

Constraints on Attractor Models of Inflation and Reheating from Planck, BICEP/Keck, ACT DR6, and SPT-3G Data

We analyze the latest cosmic microwave background (CMB) constraints on the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from Planck 2018, BICEP/Keck 2018, the Atacama Cosmology Telescope Data Release 6 (ACT DR6), and the South Pole Telescope (SPT-3G) data, focusing on their implications for attractor models of inflation. We compare systematically observational bounds with theoretical predictions for both E-model ($\alpha$-Starobinsky) and T-model potentials. The observational constraints accommodate E-models with $\alpha \lesssim 25$, with the canonical Starobinsky model ($\alpha = 1$) predicting $n_s = 0.958-0.963$ for reheating temperatures between $100 - 10^{10}$ GeV, in good agreement with Planck 2018 data and within the 95% CL region determined by the Planck-ACT-SPT combination, but below the 95% confidence region of the Planck-ACT-DESI combination. Higher reheating temperatures from near-instantaneous reheating improve the compatibility. T-models predict slightly lower $n_s$ values (0.956-0.961), in some tension with Planck 2018 data, and we find an upper limit of $\alpha \lesssim 11$ in these models. We extend our analysis to generalized $\alpha$-attractors with monomial potentials $V(\varphi) \propto \varphi^k$ near the minimum, demonstrating that models with $k \geq 6$ naturally predict $n_s \simeq 0.965 - 0.968$ for typical number of $e$-folds, in better agreement with the ACT DR6 data. We also consider deformed E- and T-models, which allow significantly higher values of $n_s$ for low values of $\alpha \simeq 1$.

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arXiv2025

Gravitational Waves from Spectator Scalar Fields

We propose a novel mechanism for gravitational wave (GW) production sourced by spectator scalar fields during inflation. These fields, while not driving cosmic expansion, generate blue-tilted isocurvature fluctuations that naturally satisfy current CMB constraints at large scales while producing enhanced power spectra at smaller scales accessible to GW detectors. The resulting GW spectrum spans an exceptionally broad frequency range from $10^{-20}$ to $1$ Hz, with amplitudes ranging from $\Omega_{\text{GW}}h^2 \sim 10^{-20}$ to $10^{-12}$ depending on the reheating temperature and spectator field mass. For heavy spectator fields with effective masses near the inflationary Hubble scale $H_I$, the mechanism produces observable signals across multiple detector bands accessible to pulsar timing arrays, space-based interferometers, and ground-based detectors. Our analysis reveals multiple complementary constraints on spectator field parameters. GW-induced limits on the effective number of relativistic species ($\Delta N_{\text{eff}}$) require $m_\chi \gtrsim 0.61 H_I$, stronger than CMB isocurvature bounds alone ($m_\chi \gtrsim 0.54 H_I$). The non-observation of primordial B-modes by \textit{Planck} provides stronger constraints $m_\chi \gtrsim 0.66 H_I$, with projected LiteBIRD sensitivity potentially reaching $m_\chi \gtrsim 0.70 H_I$. This mechanism enables a unique multi-messenger probe of beyond the Standard Model physics during inflation, providing simultaneous constraints on inflationary dynamics, dark matter production, and reheating through current and next-generation GW experiments.

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arXiv2025

The Electroweak Sphaleron Revisited: I. Static Solutions, Energy Barrier, and Unstable Modes

The electroweak sphaleron is a static, unstable solution of the Standard Model classical field equations, representing the energy barrier between topologically distinct vacua. In this work, we present a comprehensive updated analysis of the sphaleron using current Standard Model parameters with the physical Higgs boson mass of $m_H = 125.1$ GeV and $m_W = 80.4$ GeV, rather than the $m_H = m_W$ approximation common in earlier studies. The study includes: (i) a complete derivation of the $SU(2)\times U(1)$ electroweak Lagrangian and field equations without gauge fixing constraints, (ii) high-precision numerical solutions for the static sphaleron configuration yielding a sphaleron energy $E_{\rm{sph}} \simeq 9.1$ TeV, (iii) an analysis of the minimum energy path in field space connecting the sphaleron to the vacuum (a 1D potential barrier as a function of Chern-Simons number), and (iv) calculation of the sphaleron single unstable mode with negative eigenvalue $\omega^2_{-} = -2.7m^2_W$, providing analytical fits for its eigenfunction. We find that using the measured Higgs mass modifies the unstable mode frequency, with important implications for baryon number violation rates in both early universe cosmology and potential high-energy collider signatures. These results provide essential input for accurate lattice simulations of sphaleron transitions and precision calculations of baryon number violation processes.

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arXiv2025

The Electroweak Sphaleron Revisited: II. Study of Decay Dynamics

We present a comprehensive analysis of electroweak sphaleron decay dynamics, employing both analytical techniques and high-resolution numerical simulations. Using a spherically symmetric ansatz, we reformulate the system as a $(1+1)$-dimensional problem and analyze its stability properties with current Standard Model parameters ($m_H = 125.1$ GeV, $m_W = 80.4$ GeV). We identify precisely one unstable mode with eigenvalue $\omega_{-}^2 \simeq -2.7m_W^2$ and numerically evolve the full non-linear field equations under various initial conditions. Through spectral decomposition, we quantify the particle production resulting from the sphaleron decay. Our results demonstrate that the decay process is dominated by transverse gauge bosons, which constitute approximately 80% of the total energy and multiplicity, while Higgs bosons account for only 7-8%. On average, the sphaleron decays into 49 $W$ bosons and 4 Higgs bosons. The particle spectra consistently peak at momenta $k \sim 1 - 1.5 \, m_W$, reflecting the characteristic size of the sphaleron. Remarkably, these properties remain robust across different decay scenarios, suggesting that the fundamental structure of the sphaleron, rather than specific triggering mechanisms, determines the decay outcomes. These findings provide distinctive experimental signatures of non-perturbative topological transitions in the electroweak theory, with significant implications for baryon number violation in the early universe and potentially for high-energy collider physics.

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arXiv2025

Scalar Field Fluctuations and the Production of Dark Matter

One of the simplest possible candidates for dark matter is a stable scalar singlet beyond the Standard Model. If its mass is below the Hubble scale during inflation, long-wavelength modes of this scalar will be excited during inflation, and their subsequent evolution may lead to the correct relic density of dark matter. In this work, we provide a comprehensive analysis of the evolution of a spectator scalar. We examine three cases: (1) a non-interacting massive scalar, (2) a massive scalar with self-interactions of the form $\lambda_\chi \chi^p$, and (3) a massive scalar coupled to the inflaton $\phi$ through an interaction term of the form $\sigma_{n,m} \phi^n \chi^m$. In all cases, we assume minimal coupling to gravity and compare these results with the production of short-wavelength modes arising from single graviton exchange. The evolution is tracked during the reheating phase. Our findings are summarized using $(m_\chi, T_{\rm RH})$ parameter planes, where $m_\chi$ is the mass of the scalar field and $T_{\rm RH}$ is the reheating temperature after inflation. The non-interacting scalar is highly constrained, requiring $m_\chi > 3 \times 10^{12}~\rm {GeV}$ and $ T_{\rm RH} \lesssim 7~\text{TeV}$ for an inflationary potential with a quadratic minimum. However, when self-interactions or couplings to the inflaton are included, the viable parameter space expands considerably. In these cases, sub-GeV and even sub-eV scalar masses can yield the correct relic abundance, opening new possibilities for light dark matter candidates. In all cases, we also impose additional constraints arising from the production of isocurvature fluctuations, the prevention of a secondary inflationary phase triggered by the spectator field, and the fragmentation of scalar condensates.

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arXiv2024

Nonminimal Superheavy Dark Matter

We investigate the gravitational production of superheavy scalar fields with nonminimal coupling during and after inflation. We derive analytical approximations using the mode function solution in a de Sitter background and also apply the steepest descent method. We study both positive and negative nonminimal couplings and show that their comoving number density spectra behave differently in the short and long wavelength regimes. We numerically compute the comoving number density spectra and dark matter abundance for a broad range of superheavy spectator fields exceeding the Hubble scale during inflation, with $m_{\chi} > H_I$, and nonminimal couplings ranging from $-300 \leq \xi \leq 300$. When computing the allowed dark matter parameter space, we impose the maximum reheating temperature constraint, the Big Bang nucleosynthesis constraint, and the isocurvature constraint. We show that the presence of a positive or negative coupling $\xi$ can expand the parameter space up to $3$ orders of magnitude above the Hubble inflationary scale, allowing such dark matter candidates to be as heavy as $\sim 10^{16} \, \rm{GeV}$ in the Starobinsky model of inflation.

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arXiv2024

Inflaton Production of Scalar Dark Matter through Fluctuations and Scattering

We study the effects on particle production of a Planck-suppressed coupling between the inflaton and a scalar dark matter candidate, $χ$. In the absence of this coupling, the dominant source for the relic density of $χ$ is the long wavelength modes produced from the scalar field fluctuations during inflation. In this case, there are strong constraints on the mass of the scalar and the reheating temperature after inflation from the present-day relic density of $χ$ (assuming $χ$ is stable). When a coupling $σϕ^2 χ^2$ is introduced, with $σ= {\tilde σ} m_ϕ^2/ M_P^2 \sim 10^{-10} {\tilde σ}$, where $m_ϕ$ is the inflaton mass, the allowed parameter space begins to open up considerably even for ${\tilde σ}$ as small as $\gtrsim 10^{-7}$. For ${\tilde σ} \gtrsim \frac{9}{16}$, particle production is dominated by the scattering of the inflaton condensate, either through single graviton exchange or the contact interaction between $ϕ$ and $χ$. In this regime, the range of allowed masses and reheating temperatures is maximal. For $0.004 < {\tilde σ} < 50$, constraints from isocurvature fluctuations are satisfied, and the production from parametric resonance can be neglected.

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arXiv2024

Astrometric Detection of Ultralight Dark Matter

Ultralight dark matter induces time-dependent perturbations in the spacetime metric, enabling its gravitational direct detection. In this work, we propose using astrometry to detect dark matter. After reviewing the calculation of the metric in the presence of scalar dark matter, we study the influence of the perturbations on the apparent motion of astrophysical bodies. We apply our results to angular position measurements of quasars, whose vast distances from Earth present an opportunity to discover dark matter with a mass as low as $10^{-33} \, \mathrm{eV} $. We explore the prospects of very long baseline interferometry and optical astrometric survey measurements for detecting ultralight relics, finding that for the smallest masses, current astrometric surveys can detect dark matter moving locally with a velocity of $10^{-3}$ with energy density as low as $10 ^{ - 4} ~{\rm GeV} / {\rm cm} ^3 $.

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arXiv2024

Gravitational Production of Heavy Particles during and after Inflation

We investigate the gravitational production of a scalar field $χ$ with a mass exceeding the Hubble scale during inflation $m_χ\gtrsim H_I$, employing both analytical and numerical approaches. We demonstrate that the steepest descent method effectively captures the epochs and yields of gravitational production in a compact and simple analytical framework. These analytical results align with the numerical solutions of the field equation. Our study covers three spacetime backgrounds: de Sitter, power-law inflation, and the Starobinsky inflation model. Within these models, we identify two distinct phases of particle production: during and after inflation. During inflation, we derive an accurate analytic expression for the particle production rate, accounting for a varying Hubble rate. After inflation, the additional burst of particle production depends on the inflaton mass around its minimum. When this mass is smaller than the Hubble scale during inflation, $H_I$, there is no significant extra production. However, if the inflaton mass is larger, post-inflation production becomes the dominant contribution. Furthermore, we explore the implications of gravitationally produced heavy fields for dark matter abundance, assuming their cosmological stability.

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arXiv2024

Inflaton decay in No-Scale Supergravity and Starobinsky-like models

We consider the decay of the inflaton in Starobinsky-like models arising from either an $R+R^2$ theory of gravity or $N=1$ no-scale supergravity models. If Standard Model matter is simply introduced to the $R + R^2$ theory, the inflaton (which appears when the theory is conformally transformed to the Einstein frame) couples to matter predominantly in Standard Model Higgs kinetic terms. This will typically lead to a reheating temperature of $\sim 3 \times 10^9$~GeV. However, if the Standard Model Higgs is conformally coupled to curvature, the decay rate may be suppressed and vanishes for a conformal coupling $ξ= 1/6$. Nevertheless, inflaton decays through the conformal anomaly leading to a reheating temperature of order $10^8$~GeV. The Starobinsky potential may also arise in no-scale supergravity. In this case, the inflaton decays if there is a direct coupling of the inflaton to matter in the superpotential or to gauge fields through the gauge kinetic function. We also discuss the relation between the theories and demonstrate the correspondence between the no-scale models and the conformally coupled $R+R^2$ theory (with $ξ= 1/6$).

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arXiv2024

Cosmological Collider Signatures of Higgs-$R^2$ Inflation

We study the cosmological collider signatures in the Higgs-$R^2$ inflation model. We consider two distinct types of signals: one originating from the inflaton coupling to Standard Model fermions and gauge bosons, and another arising from the isocurvature mode interaction with the inflaton. In the former case, we determine that the signal magnitude is likely too small for detection by upcoming probes, primarily due to suppression by both the Planck scale and slow-roll parameters. However, we provide a detailed computation of the signal which could be potentially applicable to various Higgs inflation variants. For the isocurvature mode signals, we observe that the associated couplings remain unsuppressed when the isocurvature mode is relatively light or comparable to the inflationary scale. In this case, we study the Higgs-$R^2$ inflation parameter space that corresponds to the quasi-single-field inflation regime and find that the signal strength could be as large as $|f_{\rm NL}| > 1$, making Higgs-$R^2$ inflation a viable candidate for observation by future 21-cm surveys.

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arXiv2024

A New Window into Gravitationally Produced Scalar Dark Matter

Conventional scenarios of purely gravitationally produced dark matter with masses below the Hubble parameter at the end of inflation are in tension with Cosmic Microwave Background (CMB) constraints on the isocurvature power spectrum. We explore a more general scenario with a non-minimal coupling between the scalar dark matter field and gravity, which allows for significantly lighter scalar dark matter masses compared to minimal coupling predictions. By imposing relic abundance, isocurvature, Lyman-$α$, and Big Bang Nucleosynthesis (BBN) constraints, we show the viable parameter space for these models. Our findings demonstrate that the presence of a non-minimal coupling expands the parameter space, yielding a dark matter mass lower bound of $2 \times 10^{-4} \, \rm{eV}$.

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