Inflationary Scale Research Articles

Issues in Palatini R2 inflation: Bounds on the reheating temperature

We consider ${\mathcal{R}}^{2}$ inflation in Palatini gravity, in the presence of scalar fields coupled to gravity. These theories, in the Einstein frame, and for one scalar field $h$, share common features with $K$-inflation models. We apply this formalism for the study of single-field inflationary models, whose potentials are monomials, $V\ensuremath{\sim}{h}^{n}$, with $n$ a positive even integer. We also study the Higgs model nonminimally coupled to gravity. With ${\mathcal{R}}^{2}$ terms coupled to gravity as $\ensuremath{\sim}\ensuremath{\alpha}{\mathcal{R}}^{2}$, with $\ensuremath{\alpha}$ constant, the instantaneous reheating temperature ${T}_{ins}$, is bounded by ${T}_{ins}\ensuremath{\le}0.290{m}_{\text{Planck}}/{\ensuremath{\alpha}}^{1/4}$, with the upper bound being saturated for large $\ensuremath{\alpha}$. For such large $\ensuremath{\alpha}$ need go beyond slow roll to calculate reliably the cosmological parameters, among these the end of inflation through which ${T}_{ins}$ is determined. In fact, as the inflaton rolls towards the end of the inflation point, the quartic in the velocity terms, unavoidable in Palatini gravity, play a significant role and cannot be ignored. The values of $\ensuremath{\alpha}$, and other parameters, are constrained by cosmological data, setting bounds on the inflationary scale ${M}_{s}\ensuremath{\sim}1/\sqrt{\ensuremath{\alpha}}$ and the reheating temperature of the Universe.

Catch-me-if-you-can: the overshoot problem and the weak/inflation hierarchy

We study the overshoot problem in the context of post-inflationary string cosmology (in particular LVS). LVS cosmology features a long kination epoch as the volume modulus rolls down the exponential slope towards the final minimum, with an energy density that scales as {m}_s^4 . It is a known fact that such a roll admits attractor tracker solutions, and if these are located the overshoot problem is solved. We show that, provided a sufficiently large hierarchy exists between the inflationary scale and the weak scale, this will always occur in LVS as initial seed radiation grows into the tracker solution. The consistency requirement of ending in a stable vacuum containing the weak hierarchy therefore gives a preference for high inflationary scales — an anthropic argument, if one likes, for a large inflation/weak hierarchy. We discuss various origins, both universal and model-dependent, of the initial seed radiation (or matter). One particularly interesting case is that of a fundamental string network arising from brane inflation — this may lead to an early epoch in which the universe energy density principally consists of gravitational waves, while an LVS fundamental string network survives into the present universe.

EV Hubble scale inflation with a radiative plateau: Very light inflaton, reheating, and dark matter in B−L extensions

We study radiative plateau-like inflation \& Z$_{BL}$-portal freeze-in fermionic dark matter (DM) in a minimal B-L extended model. The U(1)$_{B-L}$ Higgs, responsible for heavy neutrino masses, also drives inflation in the early universe, thanks to radiative corrections from the heavy neutrinos \& the Z$_{BL}$ gauge boson. In our benchmark choice for the U(1)$_{B-L}$ gauge coupling $g_{B-L}\sim10^{-4}$, a light Z$_{BL}$ boson can be explored by current and future lifetime frontier experiments, such as FASER and FASER 2 at the LHC, SHiP, Belle II and LHCb. For the benchmark, the Hubble scale of inflation ($\mathcal{H}_{inf}$) is very low ($\mathcal{H}_{inf} = \mathcal{O}(100)$ eV) \& the inflaton turns out to be very light with mass of $\mathcal{O}(1)$ eV, and consequently the decay width of inflaton is extremely small. We investigate a 2-field system with the inflaton/B-L Higgs and the Standard Model (SM) Higgs, and find that the reheating with a suffuciently high temperature occurs when the water-fall direction to the SM Higgs direction opens up in the trajectory of the scalar field evolution.

Asymptotically free and safe quantum gravity scenarios consistent with Hubble, laboratory, and inflation scale physics

To find out the possible scenarios for quantum gravity consistent with the observed universe, we numerically investigate the non-perturbative renormalization group equations of a general quadratic gravity theory recently derived by Sen, Wetterich and Yamada (\textit{JHEP} 03 (2022) 130). As boundary conditions, we impose consistency with the Hubble scale and the laboratory scale experiments, and the Starobinsky model of inflation. We find two kinds of trajectories which go to different regime at the trans-Planckian scales: i) a trajectory which flows to the asymptotically free regime, and ii) a trajectory which flows to the asymptotically safe regime. To determine the early-time cosmological scenario, an additional observational data from beyond the homogeneous and isotropic space-time is necessary.

Inflaton-driven early dark energy

By arranging the control parameters, we examine whether the mass varying neutrino model PRD 103, 063540 (2021), enabling one to unify inflation with the present dark energy, can be used for producing an early dark energy. The model works in the following way. At early stages of the Big-Bang, the inflation trapped in the minimum at ϕ=0 gets uplifted due to interaction with neutrinos and starts to roll down to one of the degenerate minima of the effective potential and after a while gets anchored at this minimum, which in turn evolves in time very slowly. Correspondingly, the early dark energy taking place as a result of this dynamical symmetry breaking also varies in time very slowly. Shortly before the recombination epoch, however, the symmetry is restored and early dark energy disappears. A typical problem of the mass varying neutrino models is that they can hardly provide the needed amount of early dark energy at the tree-level because of smallness of neutrino masses. Nevertheless, the quantum fluctuations of ϕ can do the job in providing sufficient early dark energy under assumption that inflationary energy scale is of the order of 1TeV. Radiative as well as thermal corrections coming from the neutrino sector do not affect the model significantly. As for the gravity induced corrections to the effective potential — they can be safely ignored.

Cosmic Inflation and Genetic Algorithms

AbstractLarge classes of standard single‐field slow‐roll inflationary models consistent with the required number of e‐folds, the current bounds on the spectral index of scalar perturbations, the tensor‐to‐scalar ratio, and the scale of inflation can be efficiently constructed using genetic algorithms. The setup is modular and can be easily adapted to include further phenomenological constraints. A semi‐comprehensive search for sextic polynomial potentials results in viable models for inflation. The analysis of this dataset reveals a preference for models with a tensor‐to‐scalar ratio in the range . We also consider potentials that involve cosine and exponential terms. In the last part we explore more complex methods of search relying on reinforcement learning and genetic programming. While reinforcement learning proves more difficult to use in this context, the genetic programming approach has the potential to uncover a multitude of viable inflationary models with new functional forms.

Imprint of primordial gravitational wave with extremely low frequency on gravitational lens system

ABSTRACT Primordial gravitational waves with extremely low frequency are expected to origin from inflation in the early Universe. The detection of such kind of gravitational waves is of great significance to verify the inflationary theory and determine the energy scale of inflation. The B mode of polarization of cosmic microwave background shows to be a promising probe of extremely low frequency primordial gravitational wave. In order to find a complementary observational feature induced by primordial gravitational wave with extremely low frequency, we propose an alternative way of detection by investigating the effect of primordial gravitational wave with extremely low frequency on a gravitational lens system with a non-aligned source–deflector–observer configuration. The results show that, with a series of chosen parameters, a gravitational lens system with perturbation from extremely low frequency primordial gravitational wave could induce time delay that could deviate from the time delay deduced from the theoretical model as much as 100 per cent, meaning that a gravitational lens system with a non-aligned configuration could serve as a potential long-baseline detector of extremely low frequency primordial gravitational wave.

Primordial clocks within stochastic gravitational wave anisotropies

A first order phase transition in the early universe can give an observable stochastic gravitational background (SGWB), which will necessarily have primordial anisotropies across the sky. In multi-field inflationary scenarios, these anisotropies may have a significant isocurvature component very different from adiabatic fluctuations, providing an alternate discovery channel for high energy physics at inflationary scales. Here, we consider classically oscillating heavy fields during inflation that can imprint distinctive scale-invariance-breaking features in the power spectrum of primordial anisotropies. While such features are highly constrained in the cosmic microwave background, we show that their amplitude can be observably large in isocurvature SGWB, despite both probing a similar period of inflation. Measuring SGWB multipoles at the required level, ℓ ∼ \U0001d4aa(10-100), will be technologically challenging. However, we expect that early detection of a strong isotropic SGWB, and the guarantee of anisotropies, would spur development of next generation detectors with sufficient sensitivity, angular resolution, and foreground discrimination.

Initial conditions for the scalaron dark matter

The scalaron of the metric f(R) gravity can constitute dark matter if its mass is in the range 4 meV ≲ m ≲ 1 MeV. We give an overview of such f(R) gravity theory minimally coupled to the Standard Model. Similarly to other dark-matter models based on scalar fields, this model has the issue of initial conditions. Firstly, the initial conditions for the scalaron are to be tuned in order to produce the observed amount of dark matter. Secondly, the primordial spatial inhomogeneities in the field are to be sufficiently small because they generate entropy (or isocurvature) perturbations, which are constrained by observations. We consider these issues in the present paper. The initial conditions for the scalaron presumably emerge at the inflationary stage. We point out that the homogeneous part of the scalaron initial value is largely unpredictable because of quantum diffusion during inflation. Thus, to account for the observed amount of dark matter, one has to resort to anthropic considerations. Observational constraints on the primordial spatial inhomogeneity of the scalaron are translated into upper bounds on the energy scale of inflation, which happen to be low but not too restrictive.

Radiative plateau inflation with conformal invariance: Dynamical generation of electroweak and seesaw scales

We investigate a scale-invariant $B-L$ scenario where the Standard Model (SM) is supplemented with a dark scalar $\phi$ which has gauge \& Yukawa interactions, with the couplings $g_{BL}$ and $y$, respectively, leading to radiative plateau inflation at scale $\phi=M$ in the ultraviolet (UV), while dynamically generating the Electroweak and Seesaw scales \textit{\'a l\'a} Coleman-Weinberg in the infrared (IR). This is particularly achieved by implementing threshold corrections at an energy scale $\mu_T$ arising due to the presence of vector-like fermions. We show that implementing the inflationary observables makes the couplings solely dependent on the plateau scale $M$, leaving us with only two independent parameters $M$ and $\mu_T$. Within the theoretically consistent parameter space defined by $m_{Z_{BL}} > 850~\rm GeV$, from the assumption of independent evolution of the dark sector couplings from the SM couplings and $M < 5.67~M_P$ required for the realisation of inflationary \textit{plateau-like} behaviour of the potential around $\phi=M$, where $M_P=2.4\times10^{18}$ GeV is the reduced Planck mass, we identify the parameter space that is excluded by the current LHC results from the search for the heavy $Z_{BL}$ boson. For typical benchmark points in the viable parameter regions, we estimate the reheating temperature to be $\mathcal{O}(TeV)$ thus consistent with the standard Big Bang Nucleosynthesis (BBN) constraints. For typical benchmark points ($M=5.67,~1,~0.1~M_P$) we predict the scales of inflation to be $\mathcal{H}_{inf}=2.79\times10^{12}$ GeV, $1.53\times10^{10}$ GeV and $1.53\times10^7$ GeV, respectively.

Gravitational wave and CMB probes of axion kination

Rotations of an axion field in field space provide a natural origin for an era of kination domination, where the energy density is dominated by the kinetic term of the axion field, preceded by an early era of matter domination. Remarkably, no entropy is produced at the end of matter domination and hence these eras of matter and kination domination may occur even after Big Bang Nucleosynthesis. We derive constraints on these eras from both the cosmic microwave background and Big Bang Nucleosynthesis. We investigate how this cosmological scenario affects the spectrum of possible primordial gravitational waves and find that the spectrum features a triangular peak. We discuss how future observations of gravitational waves can probe the viable parameter space, including regions that produce axion dark matter by the kinetic misalignment mechanism or the baryon asymmetry by axiogenesis. For QCD axion dark matter produced by the kinetic misalignment mechanism, a modification to the inflationary gravitational wave spectrum occurs above 0.01 Hz and, for high values of the energy scale of inflation, the prospects for discovery are good. We briefly comment on implications for structure formation of the universe.

Small cosmological constant from a peculiar inflaton potential

We propose a novel scenario to explain the small cosmological constant (CC) by a finely tuned inflaton potential. The tuned shape is stable under radiative corrections, and our setup is technically natural. The peculiar po- tential approximately satisfies the following conditions: the inflation is eternal if CC is positive, and not eternal if CC is negative. By introducing a slowly varying CC from a positive value to a negative value, the dominant volume of the Universe after the inflation turns out to have a vanishingly small CC. The scenario does not require eternal inflation but the e-folding number is exponentially large and the inflation scale should be low enough. The scenario can have a consistent thermal history, but the present equation of state of the Universe is predicted to differ from the prediction of the {\Lambda}CDM model. A concrete model with a light scalar field is studied.

Measuring the inflaton coupling in the CMB

We study the perspectives to extract information about the microphysical parameters that governed the reheating process after cosmic inflation from CMB data. We identify conditions under which the inflaton coupling to other fields can be constrained for a given model of inflation without having to specify the details of the particle physics theory within which this model is realised. This is possible when the effective potential during reheating is approximately parabolic, and when the coupling constants are smaller than an upper bound that is determined by the ratios between the inflaton mass and the Planck mass or the scale of inflation. We consider scalar, Yukawa, and axion-like interactions and estimate that these conditions can be fulfilled if the inflaton coupling is comparable to the electron Yukawa coupling or smaller, and if the inflaton mass is larger than 105 GeV. Constraining the order of magnitude of the coupling constant requires measuring the scalar-to-tensor ratio at the level of 10-3, which is possible with future CMB observatories. Such a measurement would provide an important clue to understand how a given model of inflation may be embedded into a more fundamental theory of nature.

BICEP/Keck data and quadratic gravity

The recent results of the BICEP and Keck collaborations have put stringent bounds on many inflationary models, including some well-motivated ones. This is certainly the case when gravity remains described by Einstein's theory up to the inflationary scale, but can be avoided by introducing quadratic-in-curvature terms that are effective at that scale. Recently it has also been shown that these terms can UV complete gravity respecting stability and unitarity. Here the predictions of such quadratic gravity are computed and compared with the BICEP/Keck constraints by focusing on some of the inflationary scenarios that are best-motivated from the particle physics point of view and are already ruled out in Einstein gravity: (critical) Higgs inflation and natural inflation. The first scenario can be considered as the most economical option as the inflaton is identified with the only known elementary scalar field in the Standard Model and the near criticality of the Standard Model is used to remain in the perturbative regime. In the second one a pseudo-Nambu-Goldstone boson contributes to the inflationary dynamics and its potential is naturally flat. It is shown that in both scenarios one can restore the agreement with the observational constraints in quadratic gravity.

Tracking down the route to the SM with inflation and gravitational waves

We explore supersymmetric SO(10) models predicting observable proton decay and various topological defects which produce different shapes and strengths of gravitational wave backgrounds depending on the scales of intermediate symmetry breaking and inflation as well. We compare these to their non-supersymmetric counterparts. By identifying the scales at which gravitational wave signals appear, we would be able to track down a particular breaking chain and discern if it has a supersymmetric origin or not. It would also be useful to observe gravitational waves from more than one source among all possible topological defects and first order phase transitions for a realistic breaking chain. For these purposes, we work out specific examples in which the grand unification and relevant intermediate scales are calculable explicitly. It turns out that examples with gravitational waves from different sources are quite difficult to obtain, and the predicted gravitational wave profiles from domain walls and first order phase transitions obtained in some examples will require detectors in the kHz to MHz region.

Classical cosmological collider physics and primordial features

Features in the inflationary landscape can inject extra energies to inflation models and produce on-shell particles with masses much larger than the Hubble scale of inflation. This possibility extends the energy reach of the program of cosmological collider physics, in which signals associated with these particles are generically Boltzmann-suppressed. We study the mechanisms of this classical cosmological collider in two categories of primordial features. In the first category, the primordial feature is classical oscillation, which includes the case of coherent oscillation of a massive field and the case of oscillatory features in the inflationary potential. The second category includes any sharp feature in the inflation model. All these classical features can excite unsuppressed quantum modes of other heavy fields which leave observational signatures in primordial non-Gaussianities, including the information about the particle spectra of these heavy degrees of freedom.

Absence of the Higuchi bound in a family of alternative linear massive spin-2 models

There is a well known result from the Fierz–Pauli (FP) theory in de Sitter background, it is the existence of a lower bound for the mass m of the spin 2 particle, the Higuchi bound. It establishes that m 2 ⩾ 2H 2, where H is the Hubble parameter, in order to the theory presents no ghost-like instabilities. In this sense, m should be unacceptable high in order to fulfill this condition at the time of the inflationary epoch of the Universe, posing a difficulty to conciliate the FP theory with cosmology. In this article we show that the Higuchi bound can be circumvented in an alternative description of massive spin-2 particles known as models. In maximally symmetric spaces the theory has two free parameters which can be consistently chosen in order to make the model absent of a lower bound for m. Then, m can be arbitrarily smaller than the energy scale of inflation avoiding instabilities at that time.

Dark matter production in Weyl R2 inflation

Dark matter and inflation are two key elements to understand the origin of cosmic structures in modern cosmology, and yet their exact physical models remain largely uncertain. The Weyl scaling invariant theory of gravity may provide a feasible scheme to solve these two puzzles jointly, which contains a massive gauge boson playing the role of dark matter candidate, and allows the quadratic scalar curvature term, namely $R^2$, to realize a viable inflationary mechanism in agreement with current observations. We ponder on the production of dark matters in the Weyl $R^2$ model, including the contribution from the non-perturbative production due to the quantum fluctuations from inflationary vacuum and perturbative ones from scattering. We demonstrate that there are generally three parameter ranges for viable dark matter production: (1) If the reheating temperature is larger than $10^3~\mathrm{GeV}$, the Weyl gauge boson as dark matter can be produced abundantly with mass larger than the inflation scale $\sim 10^{13}~\mathrm{GeV}$. (2) Small mass region with $3\times10^{-13}~\mathrm{GeV}$ for a higher reheating temperature. (3) Annihilation channel becomes important in the case of higher reheating temperature, which enables the Weyl gauge boson with mass up to $4\times10^{16}~\mathrm{GeV}$ to be produced through freeze-in.

Constraining α-attractor models from reheating

In this paper, we eliminate the parameters originally present in models of inflation of the [Formula: see text]-attractor type in favor of the scalar spectral index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text]. We then write expressions for the number of [Formula: see text]-folds during reheating [Formula: see text]. By imposing reasonable conditions on [Formula: see text], we can restrict [Formula: see text] and [Formula: see text] and in turn, we use these constraints in order to find bounds for cosmological quantities of interest such as the number of [Formula: see text]-folds during inflation and the radiation dominated eras, as well as for the reheating temperature and the running index. The minimum condition that [Formula: see text] must satisfy is [Formula: see text] which we use to constrain the cosmological quantities mentioned above. In particular, we find that the tensor-to-scalar ratio [Formula: see text] (and as a consequence the energy scale of inflation) is bounded from below. We provide figures illustrating the behavior of these quantities as functions of [Formula: see text] for several values of [Formula: see text] and tables containing the bounds so obtained.

Gauging the R symmetry of old minimal R+R2 supergravity

Old-minimal $R+R^2$ supergravity has a $U(1)$ R-symmetry which rotates the chiral curvature superfield. We gauge this R-symmetry and study new interactions involving the gauge multiplet in the context of inflation and supersymmetry breaking. We construct models where supersymmetry and the R-symmetry are spontaneously broken during and after Starobinsky inflation, and one-loop gauge anomalies are cancelled by the Green--Schwarz mechanism which can also generate Standard Model gaugino masses. The hierarchy between the auxiliary fields, $\langle F\rangle\gtrsim\langle D\rangle$, leads to split mass spectrum where the chiral multiplet masses are around the inflationary scale ($10^{13}$ GeV), while the gauge multiplet masses can be arbitrarily small.