Hilltop Inflation Research Articles

Reheating constraints on mutated hilltop inflation

Future research studies of cosmic microwave background (CMB) polarization seem likely to provide a more improved upper bound of [Formula: see text].03 on the tensor-to-scalar ratio (r). In this work, we present the reheating predictions of mutated hilltop inflation (MHI). We find that the model is well consistent with combined Planck+BK18+BAO observations over a range of effective equation of state (EoS) ([Formula: see text]) and model parameter ([Formula: see text]). For lower values of [Formula: see text], MHI generates considerably smaller r compared to normal hilltop potential by lying well within the observational bounds, making MHI a better choice as per recent and future observational studies.

Scaling characteristics of hilltop and hilltop-squared inflation

Scaling characteristics of hilltop and hilltop-squared inflation

Modular invariant hilltop inflation

In this paper we show that it is possible to achieve successful hilltop inflation in which the inflaton is identified as the modulus field in a modular invariant theory.The dilaton plays a crucial role in shaping the potential.Modular invariant gaugino condensation provides the mechanism for the modulus stabilisation after inflation. The inflationary trajectory lies on the lower boundary of the fundamental domain of the modulus field τ. Inflation starts near the fixed point τ = i, and ends at a point near τ = ω, which is the global de Sitter vacuum.We investigate the allowed parameter space for successful modular invariant hilltop inflation.

LiteBIRD and CMB-S4 sensitivities to reheating in plateau models of inflation

We study the sensitivity of LiteBIRD and CMB-S4 to the reheating temperature and the inflaton coupling in three types of plateau-potential models of inflation, namely mutated hilltop inflation, radion gauge inflation, and α-attractor T models. We first find relations between model parameters and CMB observables in all models. We then perform Monte Carlo Markov Chain based forecasts to quantify the information gain on the reheating temperature, the inflaton coupling, and the scale of inflation that can be achieved with LiteBIRD and CMB-S4, assuming a fiducial tensor-to-scalar ratio r̅ ∼ 0.02 and neglecting foreground contamination of the B-mode polarization spectrum. We compare the results of the forecasts to those obtained from a recently proposed simple analytic method. We find that both LiteBIRD and CMB-S4 can simultaneously constrain the scale of inflation and the reheating temperature in all three types of models. They can for the first time obtain both an upper and lower bound on the latter, comprising the first ever measurement of the big bang temperature. In the mutated hilltop inflation and radion gauge inflation models this can be translated into a measurement of the inflaton coupling in parts of the parameter space. Constraining this microphysical parameter will help to understand how these models of inflation may be embedded into a more fundamental theory of particle physics.

Postinflationary production of particle dark matter: Hilltop and Coleman-Weinberg inflation

We investigate the production of nonthermal dark matter (DM), χ, during the postinflationary reheating era. For inflation, we consider two slow roll single field inflationary scenarios—generalized version of Hilltop (GH) inflation, and Coleman-Weinberg (CW) inflation. Using a set of benchmark values that comply with the current constraints from cosmic microwave background radiation (CMBR) data for each inflationary model, we explored the parameter space involving mass of dark matter particles, mχ, and coupling between inflaton and χ, yχ. For these benchmarks, we find that tensor-to-scalar ratio r can be as small as 2.69×10−6 for GH and 1.91×10−3 for CW inflation, both well inside 1−σ contour on scalar spectral index versus r plane from 2018+BICEP3+2018 dataset, and testable by future cosmic microwave background (CMB) observations, e.g., Simons Observatory. For the production of χ from the inflaton decay satisfying CMB and other cosmological bounds and successfully explaining total cold dark matter density of the present universe, we find that yχ should be within this range O(10−4)≳yχ≳O(10−20) for both inflationary scenarios. We also show that, even for the same inflationary scenario, the allowed parameter space on reheating temperature versus mχ plane alters with inflationary parameters including scalar spectral index, r, and energy scale of inflation. Published by the American Physical Society 2024

Hilltop sneutrino hybrid inflation

In this work, we consider a hilltop version of the (supersymmetric) sneutrino hybrid inflation where the right-handed sneutrino field plays the role of the inflaton field. This model is a type III hilltop inflation that can produce a spectral index ns=0.96 which fits perfectly to experimental observations without fine-tuning of parameters. We also briefly consider nonthermal leptogenesis via the decay of the right-handed sneutrino inflaton field after inflation.

Generalized hilltop inflation

Generalized hilltop inflation

Primordial black hole production in natural and hilltop inflation

We consider the possibility of primordial black hole, PBH, formation sourced by a rise in the power spectrum. The power spectrum becomes large at late times due to decay of the inflaton into vectors through a ϕFF̃ coupling. Two background inflaton models which are well supported by current Planck data are considered, natural inflation and hilltop inflation. Many of the papers considering formation of PBHs have considered a peaked power spectrum where Pζ gets small again at late times. This avoids overproducing miniature PBHs which would evaporate and could violate BBN and CMB bounds. This paper examines the other way of avoiding these bounds, producing PBHs from perturbations formed closer to the end of inflation such that the PBHs are too small to violate these bounds. This has the advantage of allowing for simpler models in that no additional feature is needed to be added to evade constraints. Although these black holes would have evaporated, they can be close to without exceeding current BBN bounds, making it possible the signature will be revealed in the future. We calculate how the various model parameters affect the mass and number of PBHs produced. Any evidence for PBHs sourced from an inflationary power spectrum would provide evidence for inflation on a drastically different energy scale from the CMB, and thus would be highly valuable in answering what occurred during inflation.

A case study of small field inflationary dynamics in the Einstein–Gauss–Bonnet framework in the light of GW170817

We study two of the most theoretically promising models of inflation, namely Natural inflation and Mutated Hilltop inflation, in the Einstein-Gauss Bonnet(EGB) gravity framework. In this work, we try to explore these models keeping observations from GW170817 on the speed of gravitational wave to be equal to the speed of light. This has direct implications on the non-minimal coupling to the Gauss–Bonnet invariant in the action. Thus, the effective potential gets new features. We have not only analysed the inflationary dynamics, but also the reheating dynamics and finally the corresponding energy spectrum of the gravitational wave.

Constant-roll inflation from non-commutative geometry viewpoint

In this paper, we consider an inflation scenario in which the inflation roll rate, defined by [Formula: see text] is supposed to be constant and study constant-roll inflation by a scalar field with minimal coupling to gravity in the presence of non-commutative (NC) parameters. For this purpose, we use the deformation approach and obtain the corresponding Lagrangian to the model by employing new variables. Then, we find exact solutions for the inflation potential, which include power-law, quadratic hilltop, and natural inflation. Further, we discuss the effect of parameters on the inflation model in NC space.

Hilltop Inflation and Generation of Helical Magnetic Field

Primordial magnetic field generated in the inflationary era can act as a viable source for the present day intergalactic magnetic field of sufficient strength. We present a fundamental origin for such a primordial generation of the magnetic field, namely through anomaly cancellation of U(1) gauge field in quantum electrodynamics in the context of hilltop inflation. We have analysed at length the power spectrum of the magnetic field, thus generated, which turns out to be helical in nature. We have also found that magnetic power spectrum has significant scale-dependence giving rise to a non-trivial magnetic spectral index, a key feature of this model. Interestingly, there exists a large parameter space, where magnetic field of significant strength can be produced.

Squared quartic hilltop inflation

A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018 survey bounds. The reheating predictions of the corrected model are investigated and by considering the reheating temperature we further constrain the $(n_s,r)$ parameter space. It is shown that the correction terms are physically important during inflation and generally need to be accounted for when considering Hilltop models as a candidate for inflation.

Challenges for heavy QCD axion inflation

We examine the theoretical possibility for the heavy QCD axion to induce slow-roll inflation while solving the strong CP problem through the Peccei-Quinn mechanism. If the cancellation between contributions from a small-size instanton and another Peccei-Quinn symmetry breaking occurs with high accuracy, the potential can be flattened enough near its maximum to achieve hilltop inflation. This comes at the cost of severe fine-tuning of their relative size and phase, but it also allows us to relate the high quality problem of the Peccei-Quinn symmetry to the fine-tuning problem of the hilltop inflation. There are two classes of such axion hilltop inflation, each giving a different relation between the axion mass at the minimum and the decay constant. The first class predicts the relation m ϕ ∼ 10-6 f ϕ, and the axion can decay via the gluon coupling and reheat the universe. Most of the predicted parameter region will be covered by various experiments such as CODEX, DUNE, FASER, LHC, MATHUSLA, and NA62 where the production and decay proceed through the same coupling that induced reheating. The second class predicts the relation m ϕ ∼ 10-6 f 2 ϕ/M pl. In this case, the axion mass is much lighter than in the previous case, and one needs another mechanism for successful reheating. The viable decay constant is restricted to be 108 GeV ≲ f ϕ ≲ 1010 GeV, which will be probed by future experiments on the electric dipole moment of nucleons. In both cases, requiring the axion hilltop inflation results in the strong CP phase that is close to zero.

String excitation by initial singularity of inflation

We discuss excitation of string oscillation modes by an initial singularity of inflation. The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and hence it is not clear that stringy effects become significant around it. With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak’s classification. We demonstrate that the initial singularities of Starobinsky and hill top inflation, assuming the slow roll inflation to the past infinity, are strong. Hence stringy corrections are inevitable in the very early stage of these inflation models. We also find that the initial singularity of the hill top inflation could be weak for non-slow roll case.

Reheating in small-field inflation on the brane: the swampland criteria and observational constraints in light of the PLANCK 2018 results

We study cosmological inflation and its dynamics in the framework of the Randall–Sundrum II brane model. In particular, we analyze in detail four representative small-field inflationary potentials, namely Natural inflation, Hilltop inflation, Higgs-like inflation, and Exponential SUSY inflation, each characterized by two mass scales. We constrain the parameters for which a viable inflationary Universe emerges using the latest PLANCK results. Furthermore, we investigate whether or not those models in brane cosmology are consistent with the recently proposed Swampland Criteria, and give predictions for the duration of reheating as well as for the reheating temperature after inflation. Our results show that (i) the distance conjecture is satisfied, (ii) the de Sitter conjecture and its refined version may be avoided, and (iii) the allowed range for the five-dimensional Planck mass, M_5, is found to be 10^5,text {TeV}lesssim M_5lesssim 10^{12},text {TeV}. Our main findings indicate that non-thermal leptogenesis cannot work within the framework of RS-II brane cosmology, at least for the inflationary potentials considered here.

Constraints for the running index independent of the parameters of the model

By writing the running of the scalar spectral index completely in terms of the scalar index [Formula: see text] and the tensor-to-scalar ratio [Formula: see text] we are able to impose constraints to models of inflation which are independent of the parameters of the model in question. We write analytical expressions for the running index of Natural Inflation, two models of the type Mutated Hilltop Inflation and the Starobinsky model. The resulting formulae for the running depend exclusively on [Formula: see text] and/or [Formula: see text] and will keep tightening the running index further as additional conditions and observations constrain the scalar and the tensor-to-scalar indices.

Quartic hilltop inflation revisited

We implement a procedure by which the parameters present in the potential of Quartic Hilltop Inflation (QHI) are eliminated in favor of the scalar spectral index ns and the tensor-to-scalar ratio r. By doing this it is posible to obtain in a straightforward and simple way the equations of a previous analysis where an analytical treatment of QHI in the large field limit is given. This procedure also allows a more precise discussion of general properties of the model. Also, using a constraint from the reheating epoch it is possible to find bounds for the parameters of the model as well as for quantities of interest such as the running of the scalar index, the reheating temperature and the inflationary scale. Since the bounds found come from expressions given exclusively in terms of ns and r they will continue to narrow as the measurements of the observables ns and r become more sensitive.

Slow-roll inflation in f(R,T) gravity and a modified Starobinsky-like inflationary model

In this work, we studied the slow-roll approximation of cosmic inflation within the context of $f(R,T)$ gravity, where $R$ is the scalar curvature, and $T$ is the trace of the energy-momentum tensor. By choosing a minimal coupling between matter and gravity, we obtained the modified slow-roll parameters, the scalar spectral index ($n_s$), the tensor spectral index ($n_{\textrm{T}}$), and the tensor-to-scalar ratio ($r$). We computed these quantities for a general power-law potential, Natural & Quartic Hilltop inflation, and the Starobinsky model, plotting the trajectories on the $(n_s,r)$ plane. We found that one of the parameters of Natural/Hilltop models is non-trivially modified. Besides, if the coupling is in the interval $-0.5 < \alpha < 5.54$, we concluded that the Starobinsky-like model predictions are in good agreement with the last Planck measurement, but with the advantage of allowing a wide range of admissible values for $r$ and $n_{\textrm{T}}$.

Note on initial conditions for small-field inflation

We show that initial conditions for small-field inflation can be determined quantum mechanically by introducing a suitable flattened region in the scalar potential. The inflaton is then driven towards the slow-roll attractor solution exponentially fast, desensitising inflation from the initial velocity and partially evading the so-called overshoot problem. We give an explicit example in the context of hilltop inflation by introducing an ultra slow-roll plateau around the maximum of the potential and analyse its effect on the phase-space trajectories.

Swampland, trans-Planckian censorship and fine-tuning problem for inflation: tunnelling wavefunction to the rescue

The trans-Planckian censorship conjecture implies that single-field models of inflation require an extreme fine-tuning of the initial conditions due to the very low-scale of inflation. In this work, we show how a quantum cosmological proposal—namely the tunneling wavefunction—naturally provides the necessary initial conditions without requiring such fine-tunings. More generally, we show how the tunneling wavefunction can provide suitable initial conditions for hilltop inflation models, the latter being typically preferred by the swampland constraints.