Hybrid inflation faces two well-known problems: the blue spectrum of the non-supersymmetric version of the model and the fine-tuning of the initial conditions of the fields leading to sufficient inflation to account for the standard cosmological problems. They are investigated by studying the exact two-fields dynamics instead of assuming slow-roll. When the field values are restricted to be less than the reduced Planck mass, a non-negligible part of the initial condition space (around 15% depending on potential parameters) leads to successful inflation. Most of it is located outside the usual inflationary valley and organized in continuous patterns instead of being isolated as previously found. Their existence is explained and their properties are studied. This shows that no excessive fine-tuning is required for successful hybrid inflation. Moreover, by extending the initial condition space to planckian-like or super-planckian values, inflation becomes generically sufficiently long and can produce a red-tilted scalar power spectrum due to slow-roll violations. The robustness of these properties is confirmed by conducting our analysis on three other models of hybrid-type inflation in various framework: "smooth" and "shifted" inflation in SUSY and SUGRA, and "radion assisted" gauge inflation. A high percentage of successful inflation for smooth hybrid inflation (up to 80%) is observed.
We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe cosmology models, including null energy condition violating inflation, inflation with general initial conditions, and string gas cosmology, etc. For the simplest G-inflation, blue tensor spectrum also implies blue scalar spectrum. In general, the inflation models with blue tensor spectra indicate large non-Gaussianities. On the other hand, string gas cosmol…
We present a series of theoretical constraints on the potentially viable inflation models that might yield a blue spectrum for primordial tensor perturbations. By performing a detailed dynamical analysis we show that, while there exists such possibility, the corresponding phase space is strongly bounded. Our result implies that, in order to achieve a blue tilt for inflationary tensor perturbations, one may either construct a non-canonical inflation model delicately, or study the generation of primordial tensor modes beyond the standard scenario of single slow-roll field.
We discuss a mechanism of particle production during inflation that can result in a blue gravitational wave (GW) spectrum, compatible with the BICEP2 result and with the r < 0.11 limit on the tensor-to-scalar ratio at the Planck pivot scale. The mechanism is based on the production of vector quanta from a rolling pseudo-scalar field. Both the vector and the pseudo-scalar are only gravitationally coupled to the inflaton, to keep the production of inflaton quanta at an unobservable level (the overproduction of non-gaussian scalar perturbations is a generic difficulty for mechanisms that aim to g…
We construct a hybrid inflationary model associated with the superheavy scale of supersymmetric grand unified theories in which the inflaton potential is provided entirely by canonical supergravity. We find that the spectrum of adiabatic density perturbations is characterized by a strongly varying spectral index which is considerably larger than unity. Moreover, the total number of e-foldings is very limited. Implications of our analysis for other hybrid inflationary scenarios are briefly discussed.
Inflation may have been driven by a component which violated the Null-Energy Condition, thereby leading to {\it super inflation}. We provide the formalism to study cosmological perturbations when such a component is described by a scalar field with arbitrary Lagrangian. Since the background curvature grows with time, gravitational waves always have a blue spectrum. Scalar perturbations may also have a blue spectrum, {\em albeit} in single field models. We apply our formalism to the case of phantom inflation with an exponential potential (whose pole-like inflationary stage is an attractor for i…
We propose a simple realization of hybrid inflation in supergravity, which does not require any unnaturally small parameters. Inflation in this scenario is relatively short, and inflationary density perturbations fall down on large scales, which corresponds to a blue spectrum with n > 1. Superheavy strings which are formed after inflation in this scenario produce density perturbations of comparable magnitude. In this mixed perturbation (MP) model one may have microwave anisotropy produced by strings and galaxy formation due to inflationary perturbations.
We consider the inflationary model in which the inflaton $ϕ$ couples to another scalar field $χ$ via the interaction $g^2(ϕ-ϕ_0)^2χ^2$ with a small coupling constant $g$ ($g^2 \sim 10^{-7}$). We assume that there is a sequence of "trapping points" $ϕ_{0i}$ along the inflationary trajectory where particles of $χ$-field become massless and are rather effectively produced. We calculate the power spectrum of inflaton field fluctuations originated from a backreaction of $χ$-particles produced, using the Schwinger's "in-in" formalism. We show that the primary curvature power spectrum produced by the…
We discuss the possibility of explaining the recent NANOGrav results by inflationary gravitational waves (IGWs) with a blue-tilted primordial spectrum. Although such IGWs can account for the NANOGrav signal without contradicting the upper bound on the tensor-to-scalar ratio at the cosmic microwave background scale, the predicted spectrum is in strong tension with the upper bound on the amplitude of the stochastic gravitational wave background by big-bang nucleosynthesis (BBN) and the second LIGO-Virgo observation run. However, the thermal history of the Universe, such as reheating and late-tim…
The mass spectrum of the primordial black holes formed by density perturbation in the radiation-dominated era of the Randall-Sundrum type-2 cosmology is given. The spectrum coincides with standard four-dimensional one on large scales but the deviation is apparent on smaller scales. The mass spectrum is initially softer than standard four-dimensional one, while after accretion during the earliest era it becomes harder than that. We also show expected extragalactic diffuse photon background spectra varying the initial perturbation power-law power spectrum and give constraints on the blue spectra…
We examine the possibility of positive spectral index of the power spectrum of the primordial tensor perturbation produced during inflation in the light of the detection of the B-mode polarization by the BICEP2 collaboration. We find a blue tilt is in general possible when the slow-roll parameter decays rapidly. We present two known examples in which a positive spectral index for the tensor power spectrum can be obtained. We also briefly discuss other consistency tests for further studies on inflationary dynamics.
We study the preheating of gauge fields in a simple axion monodromy model and compute the induced entropy perturbations and their effect on the curvature fluctuations. We find that the correction to the spectrum of curvature perturbations has a blue spectrum with index $n_s = 5/2$. Hence, these induced modes are harmless for the observed structure of the universe. Since the spectrum is blue, there is the danger of overproduction of primordial black holes. However, we show that the observational constraints are easily satisfied.
We suggest the new feature of primordial gravitational waves sourced by the axion-gauge couplings, whose forms are motivated by the dimensional reduction of the form field in the string theory. In our inflationary model, as an inflaton we adopt two types of axion, dubbed the model-independent axion and the model-dependent axion, which couple with two gauge groups with different sign combination each other. Due to these forms both polarization modes of gauge fields are amplified and enhance both helicies of tensor modes during inflation. We point out the possibility that a primordial blue-tilte…
We present a class of very simple inflationary models of two scalar fields which leads to nongaussian isothermal perturbations with "blue" spectrum, n > 1. One of the models is inspired by supersymmetric theories where light scalar fields naturally acquire masses of the order of the Hubble constant H during inflation. Another model presumes that one of the fields has a nonminimal interaction with gravity. By a slight modification of parameters of these models one can obtain either gaussian isothermal perturbations, or nongaussian adiabatic perturbations with n > 1.
The scale invariant scalar and tensor perturbations, which are predicted from inflation, are eigenmodes in the conformal coordinates. The 'out' observer in the de Sitter space observes a thermal spectrum with a Gibbons-Hawking temperature $H/2π$ of these 'Bunch-Davies' particles. The tensor power spectrum observed in experiments can have an imprint of the Gibbons-Hawking thermal distribution due to the mode mixing between 'in' state conformal coordinates and the coordinate frame of the observer. We find that the the Bunch-Davies modes appear as thermal modes to the asymptotic Minkowski observe…
We construct a hybrid inflationary model associated with the superheavy scale of the minimal supersymmetric standard model which is based on the simplest superpotential for symmetry breaking and in which the inflaton potential along the inflationary trajectory is essentially provided by quasi-canonical supergravity. The resulting spectrum of adiabatic density perturbations is blue and the duration of inflation sufficient but rather limited.
In the inflationary cosmology it occurs frequently that the inflaton field is trapped in a local, transient minimum with non-zero vacuum energy. The difficulty regarding the curvature perturbation produced during such a stage is that classically the inflaton does not move so that the comoving hypersurfaces are not well defined at linear order in the scalar field perturbation. In this paper, assuming a mechanism of trapping which resembles a high temperature correction to the potential, we explicitly calculate for the first time the resulting power spectrum of the curvature perturbation by eval…
We propose a new class of inflationary models in which the scalar field potential governing inflation is generated by the same non-perturbative gauge dynamics that may lead to supersymmetry breaking. Such models satisfy constraints from cosmic microwave background measurements for natural values of the fundamental parameters in the theory. In addition, they have two particularly interesting characteristics: a ``blue'' spectrum of scalar perturbations, and an upper bound on the total amount of inflation possible.
In models of cosmological inflation motivated by dynamical supersymmetry breaking, the potential driving inflation may be characterized by inverse powers of a scalar field. These models produce observables similar to those typical of the hybrid inflation scenario: negligible production of tensor (gravitational wave) modes, and a blue scalar spectral index. In this short note, we show that, unlike standard hybrid inflation models, dynamical supersymmetric inflation (DSI) predicts a measurable deviation from a power-law spectrum of fluctuations, with a variation in the scalar spectral index $|dn…
We show explicitly some exciting features of double-inflation: (i) it can often lead to strongly correlated adiabatic and entropy (isocurvature) power spectra. (ii) The two-field slow-roll consistency relations can be violated when the correlation is large at Hubble crossing. (iii) The spectra of adiabatic and entropy perturbations can be strongly scale-dependent and tilted toward either the red or blue. These effects are typically due to a light or time-dependent entropy mass and a non-negligible angular velocity in field space during inflation. They are illustrated via a multi-parameter nume…
We show that vector theories on cosmological scales are excellent candidates for dark energy. We consider two different examples, both are theories with no dimensional parameters nor potential terms, with natural initial conditions in the early universe and the same number of free parameters as LCDM. The first one exhibits scaling behaviour during radiation and a strong phantom phase today, ending in a "big-freeze" singularity. This model provides the best fit to date for the SNIa Gold dataset. The second theory we consider is standard electromagnetism. We show that a temporal electromagnetic …
In the hope of avoiding model dependence of the cosmological observables, phenomenological parametrizations of Cosmic Inflation have recently been proposed. Typically, they are expressed in terms of two parameters associated with an expansion of the inflationary quantities matching the belief that inflation is characterized by two numbers only, the tensor-to-scalar ratio and the scalar spectral index. We give different arguments and examples showing that these new approaches are either not generic or insufficient to make predictions at the accuracy level needed by the cosmological data. We con…
For suitable cosmological backgrounds, thermal fluctuations of a gas of strings can generate a scale-invariant spectrum of cosmological fluctuations without requiring a phase of inflationary expansion. We highlight the key points of this mechanism, and discuss cosmological backgrounds in which this scenario can be realized. The spectrum of cosmological perturbations has a small red tilt (like in scalar field-driven inflation) but (unlike in inflation) there is a small blue tilt of the spectrum of gravitational waves.
A realistic tribrid model of sneutrino inflation is constructed in an $R$-symmetric $SU(5)$ grand unified theory (GUT). To avoid the monopole problem, a pseudosmooth inflationary trajectory is generated with the help of an additional $Z_5$ symmetry which is broken during and after inflation. The predictions of inflationary parameters are made at the central value of the scalar spectral index, $n_s =0.968$. The largest possible value of the tensor to scalar ratio, $r\lesssim 0.0027$, is obtained with sub-Planckian field values ($\lesssim m_P$). A successful realization of reheating and leptogen…
The generation of helical magnetic fields during single field inflation due to an axial coupling of the electromagnetic field to the inflaton is discussed. We find that such a coupling always leads to a blue spectrum of magnetic fields during slow roll inflation. Though the helical magnetic fields further evolve during the inverse cascade in the radiation era after inflation, we conclude that the magnetic fields generated by such an axial coupling can not lead to observed field strength on cosmologically relevant scales.
We study the production of primordial circular ("V-mode") polarization in axion inflation coupled to fermions and gauge fields, with special attention paid to (p)reheating. We construct the power spectrum of $V$, and find a blue-tilted spectrum with index $n_V=4$. This is independent of the dominant decay channel of the inflaton (direct fermion vs. direct photon production)
We discuss the waterfall that ends hybrid inflation. Making some simplifying assumptions, that may be satisfied by GUT inflation models, two issues are addressed. First, the procedure of keeping the quantum fluctuation of the waterfall field only in the regime where it can be regarded as classical. Second, the contribution to the primordial curvature perturbation that is generated during the waterfall. Because the waterfall field is heavy during inflation, the spectrum of this contribution is strongly blue and hence is negligible on cosmological scales.
In this paper the possibility of generating large scale curvature perturbations induced from the entropic perturbations during the waterfall phase transition of standard hybrid inflation model is studied. We show that whether or not appreciable amounts of large scale curvature perturbations are produced during the waterfall phase transition depend crucially on the competition between the classical and the quantum mechanical back-reactions to terminate inflation. If one considers only the classical evolution of the system we show that the highly blue-tilted entropy perturbations induce highly b…
The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-year dataset, which might be interpreted as the first detection of a stochastic gravitational wave background (SGWB). I examine whether the NANOGrav signal might be explained by an inflationary SGWB, focusing on the implications for the tensor spectral index $n_T$ and the tensor-to-scalar ratio $r$. Explaining NANOGrav while complying with upper limits on $r$ from BICEP2/Keck Array and Planck requires $r \gtrsim {\cal O}(10^{-6})$ in conjunction w…
It is known that if the Peccei-Quinn symmetry breaking field is displaced from its minimum during inflation, the axion isocurvature spectrum is generically strongly blue tilted with a break transition to a flat spectrum. We fit this spectrum (incorporated into the "vanilla" $Λ$-CDM cosmological model) to the Planck and BOSS DR11 data and find a mild hint for the presence of axionic blue-tilted isocurvature perturbations. We find the best fit parameter region is consistent with all of the dark matter being composed of QCD axions in the context of inflationary cosmology with an expansion rate of…
We analyse the dynamics of spinodal decomposition in inflationary cosmology using the closed time path formalism of out of equilibrium quantum field theory combined with the non-perturbative Hartree approximation. In addition to a general analysis, we compute the detailed evolution of two inflationary models of particular importance: lambda Phi^4 new inflation and natural inflation. We compute the metric fluctuations resulting from inflationary phase transitions in the slow roll approximation, showing that there exists a regime for which quantum fluctuations of the inflaton field result in a s…
A scenario in which inflation, dark energy and dark matter can be unified into a single scalar field, the inflaton field $ϕ$, is studied. The inflaton is identified with the sneutrino, the scalar partner of the heavy neutrino. We determine the conditions needed for avoiding the gravitino problem and not having negligible plasma effects and we obtain the allowed range for the sneutrino coupling.
We point out that a successful inflationary magnetogenesis could be realised if we break the local U(1) gauge symmetry during inflation. The effective electric charge is fixed as a fundamental constant, which allows us to obtain an almost scale invariant magnetic spectrum avoiding both the strong coupling and back reaction problems. We examine the corrections to the primordial curvature perturbation due to these stochastic electromagnetic fields and find that, at both linear and non-linear orders, the contributions from the electromagnetic field are negligible compared to those created from va…
We generalize the treatment of inflationary perturbations to deal with the non-Markovian colored noise emerging from any realistic approach to stochastic inflation. We provide a calculation of the power-spectrum of the gauge-invariant comoving curvature perturbation to first order in the slow-roll parameters. Properly accounting for the constraint that our local patch of the Universe is homogeneous on scales just above the present Hubble radius, we find a blue tilt of the power-spectrum on the largest observable scales, in agreement with the WMAP data which show an unexpected suppression of th…
We compare the standard single scalar field inflationary predictions with those of an inflationary phase driven by a tachyon field. A slow-roll formalism is defined for tachyon inflation and we derive the spectra of scalar and tensor perturbations as well as the consistency relations. At lowest order the predictions of standard and tachyon inflation are the same. Higher order deviations are present and their observational relevance is discussed. We discuss the observational consequences of some typical inflationary tachyon potentials and compare them with recent data. All the models predict a …
Single field inflation in the light of Pulsar Timing Array Data: Quintessential interpretation of blue tilted tensor spectrum through Non-Bunch Davies initial condition
We explore a new class of supersymmetric models of inflation where the inflaton is realised as a combination of a Higgs field and (gauge non-singlet) matter fields, using a "tribrid" structure of the superpotential. Inflation is associated with a phase transition around GUT scale energies. The inflationary trajectory already preselects the later vacuum after inflation, which has the advantage of automatically avoiding the production of dangerous topological defects at the end of inflation. While at first sight the models look similar to smooth inflation, they feature a waterfall and are theref…
We investigate constraints on the spectral index of primordial gravitational waves (GWs), paying particular attention to a blue-tilted spectrum. Such constraints can be used to test a certain class of models of the early Universe. We investigate observational bounds from LIGO+Virgo, pulsar timing and big bang nucleosynthesis, taking into account the suppression of the amplitude at high frequencies due to reheating after inflation and also late-time entropy production. Constraints on the spectral index are presented by changing values of parameters such as reheating temperatures and the amount …
A supersymmetric hybrid inflation framework is employed to realize a class of non-minimal inflation models with $U(1)_R \times Z_n$ global symmetry. This framework naturally incorporates models based on grand unified theories by avoiding the most commonly faced monopole problem. The predictions of inflationary observables, the scalar spectral index $n_s = 0.960-0.966$ and the tensor to scalar ratio $r=0.0031-0.0045$, are in perfect agreement with the Planck 2018 data. For sub-Planckian values of the field the $Z_n$ symmetry is only allowed for $n\leq 4$.
We study F-term hybrid inflation in a novel supersymmetric extension of the SM with a subdominant Fayet-Iliopoulos D-term. We call this particular form of inflation, in short, F_D-term hybrid inflation. The proposed model ties the mu-parameter of the MSSM to an SO(3)-symmetric Majorana mass m_N, through the vacuum expectation value of the inflaton field. The late decays of the ultraheavy particles associated with the extra U(1) gauge group, which are abundantly produced during the preheating epoch, could lower the reheat temperature even up to 1 TeV, thereby avoiding the gravitino overproducti…
We have recently proposed the idea that dark matter in our universe is formed by primordial black holes generated by Standard Model Higgs fluctuations during inflation and thanks to the fact that the Standard Model Higgs potential develops an instability at a scale of the order of $10^{11}$ GeV. In this sense, dark matter does not need any physics beyond the Standard Model, although the mechanism needs fine-tuning to avoid the overshooting of the Higgs into the dangerous AdS vacuum. We show how such fine-tuning can be naturally avoided by coupling the Higgs to a very heavy scalar with mass $\g…
We propose a model of inflation based on a simple variant of the NMSSM, called $ϕ$NMSSM where the additional singlet $ϕ$ plays the role of the inflaton in hybrid (or inverted hybrid) type models. The $ϕ$NMSSM solves the $μ$ problem of the MSSM via the vacuum expectation value of the gauge singlet N, but also solves the strong CP problem through an approximate Peccei-Quinn symmetry. The potential energy which drives inflation originates from the F-term of the effective supergravity theory which result from a generic string theory. In the class of models considered the inflaton is protected from…
We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with $B^2(k) \propto k$, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the…
Among primordial magnetogenesis models, inflation is a prime candidate to explain the current existence of cosmological magnetic fields. Assuming conformal invariance to be restored after inflation, their energy density decreases as radiation during the decelerating eras of the universe, and in particular during reheating. Without making any assumptions on inflation, on the magnetogenesis mechanism and on how the reheating proceeded, we show that requiring large scale magnetic fields to remain subdominant after inflation gives non-trivial constraints on both the reheating equation of state par…
Effects of soft SUSY-breaking terms on inflation potentials are discussed. There exist generic constraints that must be satisfied in order not for the inflaton potential to loose its flatness. We examine explicitly the constraints in the case of a hybrid inflation model and find that the coupling constant λbetween the inflaton and the ``water-fall-direction'' field is bounded as 2.0 \times 10^{-6} < λ. This is a highly non-trivial result. Indeed, if we adopt the severest constraint from avoiding the problem of the gravitinos produced non-thermally, λ< 7.4 \times 10^{-6} is required, under a re…
We estimate large-scale curvature perturbations from isocurvature fluctuations in the waterfall field during hybrid inflation, in addition to the usual inflaton field perturbations. The tachyonic instability at the end of inflation leads to an explosive growth of super-Hubble scale perturbations, but they retain the steep blue spectrum characteristic of vacuum fluctuations in a massive field during inflation. The power spectrum thus peaks around the Hubble-horizon scale at the end of inflation. We extend the usual delta-N formalism to include the essential role of these small fluctuations when…
The BICEP-2 team has reported the detection of primordial cosmic microwave background B-mode polarization, with hints of a suppression of power at large angular scales relative to smaller scales. Provided that the B-mode polarization is due to primordial gravitational waves, this might imply a blue tilt of the primordial gravitational wave spectrum. Such a tilt would be incompatible with standard inflationary models, although it was predicted some years ago in the context of a mechanism that thermally generates the primordial perturbations through a Hagedorn phase of string cosmology. The purp…
We show that, for values of the axion decay constant parametrically close to the GUT scale, the Peccei-Quinn phase transition may naturally occur during warm inflation. This results from interactions between the Peccei-Quinn scalar field and the ambient thermal bath, which is sustained by the inflaton field through dissipative effects. It is therefore possible for the axion field to appear as a dynamical degree of freedom only after observable CMB scales have become super-horizon, thus avoiding the large-scale axion isocurvature perturbations that typically plague such models. This nevertheles…
We present a mechanism for realizing hybrid inflation using two axion fields with a purely non-perturbatively generated scalar potential. The structure of scalar potential is highly constrained by the discrete shift symmetries of the axions. We show that harmonic hybrid inflation generates observationally viable slow-roll inflation for a wide range of initial conditions. This is possible while accommodating certain UV arguments favoring constraints $f\lesssim M_{\rm P}$ and $Δϕ_{60}\lesssim M_{\rm P}$ on the axion periodicity and slow-roll field range, respectively. We discuss controlled $\mat…
Previous computations of strongly blue tilted axionic isocurvature spectra were computed in the parametric region in which the lightest time-dependent mass is smaller than the Hubble expansion rate during inflation, leading to an overdamped time evolution. Here we present the strongly blue tilted axionic isocurvature spectrum in an underdamped time evolution parametric regime. Somewhat surprisingly, there exist parametric regions with a strong resonant spectral behavior that leads to a rich isocurvature spectral shape. We focus on computing this resonant spectrum analytically in a large parame…
Future astrophysical datasets promise to strengthen constraints on models of inflation, and extracting these constraints requires methods and tools commensurate with the quality of the data. In this paper we describe ModeCode, a new, publicly available code that computes the primordial scalar and tensor power spectra for single field inflationary models. ModeCode solves the inflationary mode equations numerically, avoiding the slow roll approximation. It is interfaced with CAMB and CosmoMC to compute cosmic microwave background angular power spectra and perform likelihood analysis and paramete…
The curvaton scenario predicts an almost scale-invariant spectrum of perturbations in most inflation models. We consider the possibility that renormalisable phi^4 or Planck scale-suppressed non-renormalisable curvaton potential terms may result in an observable deviation from scale-invariance. We show that if the curvaton initially has a large amplitude and if the total number of e-foldings of inflation is less than about 300 then a running blue perturbation spectrum with an observable deviation from scale-invariance is likely. D-term inflation is considered as an example with a potentially lo…
