Many models of high energy physics possess metastable vacua. It is conceivable that the universe can get trapped in such a false vacuum, irrespective of its origin and prior history, at an earlier stage during its evolution. The ensuing false vacuum inflation results in a cold and empty universe and has a generic graceful exit problem. We show that an inflection point inflation along the flat directions of the Minimal Supersymmetric Standard Model (MSSM) can resolve this graceful exit problem by inflating the bubble which nucleate out of a false vacuum. The important point is that the initial condition for an MSSM inflation can be naturally realized, due to an attractor behavior towards the inflection point. We investigate these issues in detail and also present an example where metastable vacua, hence the false vacuum inflation, can happen within the MSSM.
We consider models of inflection point inflation. The main drawback of such models is that they suffer from the overshoot problem. Namely the initial condition should be fine tuned to be near the inflection point for the universe to inflate. We show that stringy realizations of inflection point inflation are common and offer a natural resolution to the overshoot problem.
In this article we provide a new closed relationship between cosmic abundance of primordial gravitational waves and primordial blackholes originated from initial inflationary perturbations for inflection-point models of inflation where inflation occurs below the Planck scale. The current Planck constraint on tensor-to-scalar ratio, running of the spectral tilt, and from the abundance of dark matter content in the universe, we can deduce a strict bound on the current abundance of primordial blackholes to be within a range, $9.99712\times 10^{-3}<Ω_{PBH}h^{2}<9.99736\times 10^{-3}$.
We study the production of gravitational waves from primordial scalar perturbations in double-inflection-point inflation, in which one of the inflection points predicts the power spectra consistent with CMB observations at large scales and the other generates a large peak in the power spectrum of scalar perturbations at small scales. We find that the reduced gravitational waves at low frequencies can be detected by future space-based laser interferometers.
In this work, we consider inflection point inflation in the framework of running kinetic term inflation in supergravity. We study the inflationary dynamics and show that the predicted value of the scalar spectral index and tensor-to-scalar ratio can lie within the $1σ$ confidence region allowed by the result of Planck 2015.
We revisit the inflection point inflation with an extended discussion to large field values and consider the reheating effects on the inflationary predictions. Parametrizing the reheating dynamics in terms of the reheating temperature and the equation of state during inflation, we show how the observationally favored parameter space of inflection point inflation is affected by reheating dynamics. Consequently, we apply the general results to the inflation models with non-minimal coupling, such as the SM Higgs inflation and the $B-L$ Higgs inflation.
Several models of inflection point inflation with the volume modulus as the inflaton are investigated. Non-perturbative superpotentials containing two gaugino condensation terms or one such term with threshold corrections are considered. It is shown that the gravitino mass may be much smaller than the Hubble scale during inflation if at least one of the non-perturbative terms has a positive exponent. Higher order corrections to the Kahler potential have to be taken into account in such models. Those corrections are used to stabilize the potential in the axion direction in the vicinity of the i…
Motivated by the recently proposed Trans-Planckian Censorship Conjecture (TCC), we propose a gauged $B-L$ model of inflection-point inflation with axion dark matter. The Hubble scale during inflation ($H_{\rm inf}$) satisfies the TCC bound of $H_{\rm inf} \lesssim 1$ GeV, the axion dark matter scenario is free from the axion domain wall and isocurvature problems, and the axion decay constant can be larger than $10^{12}$ GeV. The seesaw mechanism is automatically incorporated in the model and the observed baryon asymmetry of the universe can be reproduced via resonant leptogenesis.
A novel inflection-point inflation model is analysed. The model considers a massless scalar field, whose self-coupling's running is stabilised by a non-renormalisable operator. The running is controlled by a fermion loop. We find that successful inflation is possible for a natural value of the Yukawa coupling $y\simeq 4\times 10^{-4}$. The necessary fine-tuning is only $\sim 10^{-6}$, which improves on the typical tuning of inflection-point inflation models, such as MSSM inflation. The model predicts a spectral index within the 1-$σ$ bound of the latest CMB observations, with negligible tensor…
We propose to address the fine tuning problem of inflection point inflation by the addition of extra vacuum energy that is present during inflation but disappears afterwards. We show that in such a case, the required amount of fine tuning is greatly reduced. We suggest that the extra vacuum energy can be associated with an earlier phase transition and provide a simple model, based on extending the SM gauge group to SU(3)_C \times SU(2)_L\times U(1)_Y\times U(1)_{B-L}, where the Higgs field of U(1)_{B-L} is in a false vacuum during inflation. In this case, there is virtually no fine tuning of t…
We provide a mechanism to obtain multiple inflection points for the inflaton potential based on the Coleman-Weinberg potential. The key ingredient is the existence of zeros of the inflaton quartic coupling beta function, which can be simply realized by a sign change of a gauge coupling beta function at a massive threshold scale in gauge-Yukawa models. A universal inflaton potential emerges for a wide range of models and can accommodate the experimental data in the small-field inflation scenario. While the ratio of tensor over scalar amplitudes is predicted to be small, the running of the scala…
We investigate the possibility to induce double peaks of gravitational wave(GW) spectrum from primordial scalar perturbations in inflationary models with three inflection points.Where the inflection points can be generated from a polynomial potential or generated from Higgs like $ϕ^4$ potential with the running of quartic coupling.In such models, the inflection point at large scales predicts the scalar spectral index and tensor-to-scalar ratio consistent with current CMB constraints, and the other two inflection points generate two large peaks in the scalar power spectrum at small scales, whic…
Inflection-point inflation is an interesting possibility to realize a successful slow-roll inflation when inflation is driven by a single scalar field with its initial value below the Planck mass ($ϕ_I \lesssim M_{Pl}$). In order for a renormalization group (RG) improved effective $λϕ^4$ potential to develop an inflection-point, the quartic coupling $λ(ϕ)$ must exhibit a minimum with an almost vanishing value in its RG evolution, namely $λ(ϕ_I) \simeq 0$ and $β_λ(ϕ_I) \simeq 0$, where $β_λ$ is the beta-function of the quartic coupling. As an example, we consider the minimal gauged $B-L$ extend…
Inflection point inflation generically includes a deviation from slow-roll when the inflaton approaches the inflection point. Such deviations are shown to be generated by transitions between singular trajectories. The effects on the power spectrum are studied within the context of universality classes for small-field models. These effects are shown to scale with universality parameters, and can explain the anomalously low power at large scales observed in the CMB. The reduction of power is related to the inflection point's basin of attraction. Implications for the likelihood of inflation are d…
Inflection-point inflation is an interesting possibility to realize a successful slow-roll inflation when inflation is driven by a single scalar field with its value during inflation below the Planck mass ($ϕ_I \lesssim M_{Pl}$). In order for a renormalization group (RG) improved effective $λϕ^4$ potential to develop an inflection-point, the running quartic coupling $λ(ϕ)$ must exhibit a minimum with an almost vanishing value in its RG evolution, namely $λ(ϕ_I) \simeq 0$ and $β_λ(ϕ_I) \simeq 0$, where $β_λ$ is the beta-function of the quartic coupling. In this paper, we consider the inflection…
Recently, it has been claimed that inflationary models with an inflection point in the scalar potential can produce a large resonance in the power spectrum of curvature perturbation. In this paper however we show that the previous analyses are incorrect. The reason is twofold: firstly, the inflaton is over-shot from a stage of standard inflation and so deviates from the slow-roll attractor before reaching the inflection. Secondly, on the (or close to) the inflection point, the ultra-slow-roll trajectory supersede the slow-roll one and thus, the slow-roll approximations used in the literature c…
We study slow roll single field inflationary scenario and the production of non-thermal fermionic dark matter, together with standard model Higgs, during reheating. For the inflationary scenario, we have considered two models of polynomial potential - one is symmetric about the origin and another one is not. We fix the coefficients of the potential from the current Cosmic Microwave Background (CMB) data from Planck/Bicep. Next, we explore the allowed parameter space on the coupling $(y_χ)$ with inflaton and mass $(m_χ)$ of dark matter (DM) particles $(χ)$ produced during reheating and satisfyi…
While ubiquitous in supersymmetric and string theory models, inflationary scenarios near an inflection point in the scalar potential generically require a severe fine-tuning of a priori unrelated supersymmetry breaking effects. We show that this can be significantly alleviated by the inclusion of dissipative effects that damp the inflaton's motion and produce a nearly-thermal radiation bath. We focus on the case where the slow-rolling inflaton directly excites heavy virtual modes that then decay into light degrees of freedom, although our main qualitative results should apply in other regimes.…
We investigate for viable models of inflation that can successfully produce dark matter (DM) from inflaton decay process, satisfying all the constraints from Cosmic Microwave Background (CMB) and from some other observations. In particular, we analyze near-inflection-point small field inflationary scenario with non-thermal production of fermionic DM from the decaying inflaton field during the reheating era. To this end, we propose two different models of inflation with polynomial potential. The potential of Model I contains terms proportional to linear, quadratic, and quartic in inflaton; wher…
We consider observational constraints and fine-tuning issues in a renormalizable model of inflection point inflation, with two independent parameters. We derive constraints on the parameter space of this model arising from the WMAP 7-year power spectrum. It has previously been shown that it is possible to successfully embed this potential in the MSSM. Unfortunately, to do this requires severe fine-tuning. We address this issue by introducing a hybrid field to dynamically uplift the potential with a subsequent smooth phase transition to end inflation at the necessary point. Large parameter regi…
We present the general discussion on the inflection point inflation with small or large inflaton fields and show the effects of reheating dynamics on the inflationary predictions. In order to compare the model predictions with precisely measured CMB anisotropies and constrain the inflation models, the knowledge of the reheating dynamics is required. Inflection point inflation extended to the trans-Planckian regime can accommodate a sizable tensor-to-scalar ratio at the detectable level in the future CMB experiments.
In this paper we will analyze generic predictions of an inflection-point model of inflation with Hubble-induced corrections and study them in light of the Planck data. Typically inflection-point models of inflation can be embedded within Minimal Supersymmetric Standard Model (MSSM) where inflation can occur below the Planck scale. The flexibility of the potential allows us to match the observed amplitude of the TT-power spectrum of the cosmic microwave background radiation with low and high multipoles, spectral tilt, and virtually mild running of the spectral tilt, which can put a bound on an …
We propose a novel scenario to produce abundant primordial black holes (PBHs) in new inflation which is a second phase of a double inflation in the supergravity frame work. In our model, some preinflation phase before the new inflation is assumed and it would be responsible for the primordial curvature perturbations on the cosmic microwave background scale, while the new inflation produces only the small scale perturbations. Our new inflation model has linear, quadratic, and cubic terms in its potential and PBH production corresponds with its flat inflection point. The linear term can be inter…
We consider critical Higgs inflation, namely Higgs inflation with a rising inflection point at smaller field values than those of the plateau induced by the non-minimal coupling to gravity. It has been proposed that such configuration is compatible with the present CMB observational constraints on inflation, and also with primordial black hole production accounting for the totality or a fraction of the observed dark matter. We study the model taking into account the NNLO corrections to the Higgs effective potential: such corrections are extremely important to reduce the theoretical error assoc…
Recently in hep-ph/0605035 and hep-ph/0608138, we have shown that primordial inflation can be embedded within the Minimal Supersymmetric Standard Model, while providing the right amplitude for the density perturbations and a tilted spectrum which matches the current data. In this short note we show that the model predicts a range of spectral tilt, $0.92 \leq n_s \leq 1$, depending on deviation from the saddle point condition. The spectral tilt saturates the lower limit when the saddle point condition is met. On the other hand the upper limit can be achieved for a slight deviation towards the p…
Inflation can occur near a point of inflection in the potential of flat directions of the Minimal Supersymmetric Standard Model. In this paper we elaborate on the complementarity between the bounds from Cosmic Microwave Background measurements, dark matter and particle physics phenomenology in determining the underlying parameters of MSSM inflation by specializing to the Minimal Supergravity scenario. We show that the future measurements from the Large Hadron Collider in tandem with all these constraints will significantly restrict the allowed parameter space. We also suggest a new perspective…
Cosmological $α$-attractors stand out as particularly compelling models to describe inflation in the very early universe, naturally meeting tight observational bounds from cosmic microwave background (CMB) experiments. We investigate $α$-attractor potentials in the presence of an inflection point, leading to enhanced curvature perturbations on small scales. We study both single- and multi-field models, driven by scalar fields living on a hyperbolic field space. In the single-field case, ultra-slow-roll dynamics at the inflection point is responsible for the growth of the power spectrum, while …
We show an analysis on the gauge-independent observables associated with two stationary configurations of the Standard Model (SM) potential (extrapolated to high energy at Next-to-Next-to-Leading-Order (NNLO)): i) the value of the top mass ensuring stability of the SM electroweak vacuum and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, keeping alive the possibility for the SM of being stable and studying applications of such configuration to models of primor…
We revisit the renormalizable polynomial inflection point model of inflation, focusing on the small field scenario which can be treated fully analytically. In particular, the running of the spectral index is predicted to be $α= -1.43 \times 10^{-3} +5.56 \times 10^{-5} \left(N_{\rm CMB}-65 \right)$, which might be tested in future. We also analyze reheating through perturbative inflaton decays to either fermionic or bosonic final states via a trilinear coupling. The lower bound on the reheating temperature from successful Big Bang nucleosynthesis gives lower bounds for these couplings; on the …
We propose a double inflection point inflationary model in supergravity with a single chiral superfield. Such a model allows for the generation of primordial black holes(PBHs) at small scales, which can account for a significant fraction of dark matter. Moreover in vacuum it is possible to give a small and adjustable SUSY breaking with a tiny cosmological constant.
We study the gauge-independent observables associated with two interesting stationary configurations of the Standard Model Higgs potential (extrapolated to high energy according to the present state of the art, namely the NNLO): i) the value of the top mass ensuring stability of the SM electroweak minimum, and ii) the value of the Higgs potential at a rising inflection point. We examine in detail and reappraise the experimental and theoretical uncertainties which plague their determination, finding that: i) stability of the SM is compatible with the present data at the 1.5 sigma level; ii) des…
The recent measurements of cosmological parameters by the Planck collaboration favors inflationary models with a redshifted spectrum and a very low tensor-to-scalar ratio. Two well-studied scenarios in the particle physics/string theory literature -- inflection point and Starobinsky inflation -- are in good agreement with these data. In these proceedings, we report on general studies of these two scenarios. We discuss similarities in their structure which, we argue, arise from a common mechanism: degenerate critical point of the potential. In particular, we emphasize their ability to support a…
The lack of power on large scales (l < 40) might have been observed by the PLANCK satellite. We argue that this putative feature can be explained by a phase of fast roll at the onset of inflation. We show that in the context of single field models what is required is an asymmetric inflection point model of which fibre inflation is a string motivated example. We study the ability of fibre inflation to generate a suppression of the CMB 2-point function power at low l, finding that the potential derived from string loops is not steep enough for this purpose. We introduce a steeper contribution to…
We show that Supersymmetric models with Type I seesaw neutrino masses support slow roll inflection point inflation. The inflaton is the D-flat direction labelled by the chiral invariant HLN composed of the Higgs(H), slepton(L) and conjugate sneutrino(N) superfields. The scale of inflation and fine tuning is set by the conjugate neutrino Majorana mass $M_{ν^c} \sim 10^6-10^{12}$ GeV. The cubic term in the (quartic) inflaton potential is dominantly from superpotential (not soft Susy breaking) couplings. The tuning conditions are thus insensitive to soft supersymmetry breaking parameters and are …
We study inflection point inflation using Singularity Theory, which relates degenerate critical points of functions to their local behavior. This approach illuminates universal features of small-field models and gives analytic control over parametrized families of scalar potentials near inflationary solutions. The behavior of the scalar potential is tied to the number of physical input parameters, which determines a set of universality classes. Within these classes, we obtain universal scaling relations for density perturbations and the scale of inflation. In specific models, we show that the …
We consider the possibility to combine inflection point inflation and growing neutrino dark energy in a particular setup of bimodal/schizophrenic neutrino model in the framework of MSSM$\otimes U(1)_{B-L}$. In order to obtain a varying neutrino mass, we make an assumption that a soft mass of $\tilde{Z'}_{BL}$ depends on a scalar field which plays the role of a cosmon field. We also investigate the possible effects of the cosmon field in the early universe such as modulated reheating and found that the induced density perturbation is negligible.
This thesis compiles the results of six works which deal with - inflationary model building and estimation of cosmological parameters from various field theoretic setup, quantification of reheating temperature, studies of leptogenesis in braneworld and estimation of primordial non-Gaussianity from ${\cal N}=1$ supergravity using $δN$ formalism. We start our discussion with exploring the possibility of MSSM inflation in the light of recent observed data from various D -flat directions using the saddle and inflection point techniques. The effective inflaton potential around saddle point and infl…
We study the cosmological properties of a metastable de Sitter vacuum obtained recently in the framework of type IIB flux compactifications in the presence of three D7-brane stacks, based on perturbative quantum corrections at both world-sheet and string loop level that are dominant at large volume and weak coupling. In the simplest case, the model has one effective parameter controlling the shape of the potential of the inflaton which is identified with the volume modulus. The model provides a phenomenological successful small-field inflation for a value of the parameter that makes the minimu…
We analyse the cosmological implications of brane-antibrane systems in string-theoretic orbifold and orientifold models. In a class of realistic models, consistency conditions require branes and antibranes to be stuck at different fixed points, and so their mutual attraction generates a potential for one of the radii of the underlying torus or the 4D string dilaton. Assuming that all other moduli have been fixed by string effects, we find that this potential leads naturally to a period of cosmic inflation with the radion or dilaton field as the inflaton. The slow-roll conditions are satisfied …
Flat directions in the Minimal Supersymmetric Standard Model (MSSM) can become unstable due to radiative corrections, and the global minimum of the (zero temperature) potential can lie at large values of the squark and/or slepton fields. Here we show that, in inflationary models of early cosmology, the universe is very likely to be in the domain of attraction of this global minimum at the end of inflation. While the minimum at the origin of field space is global at sufficiently high temperatures, depending on details of the model, the universe may be trapped in the non-zero minimum until it be…
