A simple model of quintessential inflation with the modified exponential potential exp(-αϕ) [A + (ϕ-ϕ_0)^2] is analyzed in the braneworld context. Considering reheating via instant preheating, it is shown that the evolution of the scalar field ϕfrom inflation to the present epoch is consistent with the observational constraints in a wide region of the parameter space. The model exhibits transient acceleration at late times for 0.96 < A α^2 < 1.26 and 271 < ϕ_0 α< 273, while permanent acceleration is obtained for 2.3 10^{-8} < A α^2 < 0.98 and 255 < ϕ_0 α< 273. The steep parameter αis constrained to be in the range 5.3 < α< 10.8.
A model of quintessential inflation is presented, which manages to achieve the requirements of both inflation and quintessence with natural values of the mass-scales and parameters.
I discuss why quintessential inflation model-building is more natural in the context of brane cosmology and study the dynamics of a particular model as an example.
It is argued why, contrary to expectations, steep brane-inflation cannot really help in overcoming the eta-problem of quintessential inflation model-building. In contrast it is shown that the problem is substantially ameliorated under the curvaton hypothesis. This is quantified by considering possible modular quintessential inflationary models in the context of both standard and brane cosmology.
Recently Peebles and Vilenkin proposed and quantitatively analyzed the fascinating idea that a substantial fraction of the present cosmic energy density could reside in the vacuum potential energy of the scalar field responsible for inflation (quintessential inflation). Here we compute the signature of this model in the cosmic microwave background polarization and temperature anisotropies and in the large scale structure.
We analyse the mechanism of quintessential inflation in brane world scenarios for a number of particle physics inspired scalar potentials. We constrain the parameter space of those scalar potentials and comment on the likelihood that we could discriminate these models from standard inflation, based on upcoming large scale structure and cosmic microwave background observations.
A unified approach to quintessence and inflation is investigated with the use of a single scalar field. It is argued that successful potentials have to approximate a combination of exponential and inverse power-law decline in the limit of large values of the scalar field. A class of such potentials is studied analytically and it is found that quintessential inflation is indeed possible. Successful models, not involving more than two natural mass scales, are obtained, which do not require fine-tuning of initial conditions and do not result in eternal acceleration.
In this paper, we study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. The conclusion we obtain is in favor of the model where the modular part of complex field plays the role of the inflaton whereas the argument part is the quintessence field. The numerical calculation shows that a heteroclinic orbit (solution of dynamical system) which interpolates betwe…
We describe a simple toy model for quintessential inflation where a complex scalar field described by a lagrangian with a Peccei-Quinn U(1) symmetry spontaneously broken at a high energy scale and explicitly broken by instanton effects at a much lower energy can account for both the early inflationary phase and the recent accelerated expansion of the Universe. The real part of the complex field plays the role of the inflaton whereas the imaginary part, the "axion", is the quintessence field.
We investigate the dependence of the gravitational wave spectrum from quintessential inflation on the reheating process. We consider two extreme reheating processes. One is the gravitational reheating by particle creation in the expanding universe in which the beginning of the radiation dominated epoch is delayed due to the presence of the epoch of domination of the kinetic energy of the inflaton (kination). The other is the instant preheating considered by Felder et al. in which the Universe becomes radiation dominated soon after the end of inflation. We find that the spectrum of the gravitat…
The energy spectra of gravitational waves (GW) produced in quintessential inflationary models increase in frequency and exhibit a sharp spike around 170 GHz where the associated fraction of critical energy density today stored in relic gravitons is of the order of $10^{-6}$. We contrast our findings with the spectra of ordinary inflationary models and we comment about possible detetction strategies of the spike.
We develop general criteria to construct unified frameworks for inflation and quintessence which employ a unique scalar field to drive both. By using such a minimal theoretical framework we avoid having to fine-tune couplings and mass-scales. In particular the initial conditions for quintessence are already fixed at the end of the inflationary epoch. We provide concrete realizations of the method which meet all inflationary and quintessence requirements, such as the COBE normalization and the resulting spectral index n = 0.97, which is in excellent agreement with the latest CMB data.
Attention has been recently drawn towards models in which inflation and quintessence schemes are unified. In such `quintessential inflation' models, a unique scalar field is required to play both the role of the inflaton and of the late-time dynamical cosmological constant. We address the issue of the initial conditions for quintessence in this context and find that, in the two explicit examples provided, inflation can uniquely fix them to be in the allowed range for a present day tracking.
We derive constraints on a simple quintessential inflation model, based on a spontaneously broken Phi^4 theory, imposed by the Wilkinson Microwave Anisotropy Probe three-year data (WMAP3) and by galaxy clustering results from the Sloan Digital Sky Survey(SDSS). We find that the scale of symmetry breaking must be larger than about 3 Planck masses in order for inflation to generate acceptable values of the scalar spectral index and of the tensor-to-scalar ratio. We also show that the resulting quintessence equation-of-state can evolve rapidly at recent times and hence can potentially be distingu…
Quintessential inflation describes a scenario in which both inflation and dark energy (quintessence) are described by the same scalar field. In conventional braneworld models of quintessential inflation gravitational particle production is used to reheat the universe. This reheating mechanism is very inefficient and results in an excessive production of gravity waves which violate nucleosynthesis constraints and invalidate the model. We describe a new method of realizing quintessential inflation on the brane in which inflation is followed by `instant preheating' (Felder, Kofman & Linde 1999). …
We study the possibility to construct an observationally viable scenario where both early Inflation and the recently detected accelerated expansion of the universe can be explained by using a single scalar field associated with the Tachyon. The Reheating phase becomes crucial to enable us to have a consistent cosmology and also to get a second accelerated expansion period. A discussion using an exponential potential is presented.
We present an explicit observationally acceptable model for evolution from inflation to the present epoch under the assumption that the entropy and matter of the familiar universe are from gravitational particle production at the end of inflation. This eliminates the problem of finding a satisfactory coupling of the inflaton and matter fields. Since the inflaton potential $V(ϕ)$ may be a monotonic function of the inflaton $ϕ$, the inflaton energy could produce an observationally significant effective cosmological constant, as in quintessence.
Recently, attempts have been made to understand the apparent near coincidence of the present dark energy and matter energy in terms of a dynamical attractor-like solution for the evolution of a scalar field. In these models the field couples with the dominant constituent and only acts like a cosmological constant after the onset of the matter-diminated epoch. A generic feature of such solutions, however, is the possibility of significant energy density in the scalar field during the radiation-dominated epoch. This possibility is even greater if the quintessence field begins in a kinetic-domina…
We present a model for quintessential inflation using a string modulus for the inflaton - quintessence field. The scalar potential of our model is based on generic non-perturbative potentials arising in flux compactifications. We assume an enhanced symmetry point (ESP), which fixes the initial conditions for slow-roll inflation. When crossing the ESP the modulus becomes temporarily trapped, which leads to a brief stage of trapped inflation. This is followed by enough slow roll inflation to solve the flatness and horizon problems. After inflation, the field rolls down the potential and eventual…
Assuming the existence of a 5D purely kinetic scalar field on the class of warped product spaces we investigate the possibility of mimic both an inflationary and a quintessential scenarios on 4D hypersurfaces, by implementing a dynamical foliation on the fifth coordinate instead of a constant one. We obtain that an induced chaotic inflationary scenario with a geometrically induced scalar potential and an induced quasi-vacuum equation of state on 4D dynamical hypersurfaces is possible. While on a constant foliation the universe can be considered as matter dominated today, in a family of 4D dyna…
An alternative to a cosmological constant is quintessence, defined as a slowly-varying scalar field potential V(ϕ). If quintessence is observationally significant, an epoch of inflation is beginning at the present epoch, with ϕthe slowly-rolling inflaton field. In contrast with ordinary inflation, quintessence seems to require extreme fine tuning of the potential V(ϕ). The degree of fine-tuning is quantified in various cases.
We have investigated cosmological models with a self-interacting scalar field and a dissipative matter fluid as the sources of matter. Different variables are expressed in terms of a {\it generating function}. Exact solutions are obtained for one particular choice of the {\it generating function} The potential corresponding to this generating function is a standard tree-level potential arising in the perturbative regime in quantum field theory. With suitable choice of parameters, the scale factor in our model exhibits both inflationary behaviour in the early universe as well as an accelerating…
We consider a curvaton scenario in which the late-time domination and the generation of the curvature perturbation is achieved by a non-oscillatory (NO) curvaton potential. Instead of considering the conventional curvaton oscillation, we consider ``weak trapping'' after preheating, which modifies the evolution of the curvaton density after preheating. The primordial isocurvature perturbation related to the curvaton is once converted into the fluctuation of the number density of the preheat field through inhomogeneous preheating. Then the evolution of the curvatons and the preheat field is cont…
A large class of quintessential inflationary models, recently proposed by Peebles and Vilenkin, leads to post-inflationary phases whose effective equation of state is stiffer than radiation. The expected gravitational waves logarithmic energy spectra are tilted towards high frequencies and characterized by two parameters: the inflationary curvature scale at which the transition to the stiff phase occurs and the number of (non conformally coupled) scalar degrees of freedom whose decay into fermions triggers the onset of a gravitational reheating of the Universe. Depending upon the parameters of…
We present an explicit cosmological model where inflation and dark energy both could arise from the dynamics of the same scalar field. We present our discussion in the framework where the inflaton field $ϕ$ attains a nearly constant velocity $m_P^{-1} |dϕ/dN|\equiv α+β\exp(βN)$ (where $N\equiv \ln a$ is the e-folding time) during inflation. We show that the model with $|α|<0.25$ and $β<0$ can easily satisfy inflationary constraints, including the spectral index of scalar fluctuations ($n_s=0.96\pm 0.013$), tensor-to-scalar ratio ($r<0.28$) and also the bound imposed on $Ω_ϕ$ during the nucleos…
A generic feature of cosmic quintessence models is the possibility of significant energy density in the scalar field during the radiation dominated epoch. This possibility is even greater if the quintessence field begins in a kinetic-dominated regime, for example as might be generated at the end of "quintessential inflation." As such, these models can be constrained by primordial nucleosynthesis and the epoch of photon decoupling. Here, we analyze both kinetic dominated and power-law quintessence fields (with and without a supergravity correction). We quantify the allowed initial conditions an…
The past, present and future of cosmic microwave background (CMB) anisotropy research is discussed, with emphasis on the Boomerang and Maxima balloon experiments. These data are combined with large scale structure (LSS) information and high redshift supernova (SN1) observations to explore the inflation-based cosmic structure formation paradigm. Here we primarily focus on a simplified inflation parameter set, {omega_b,omega_{cdm},Omega_{tot}, Omega_Q,w_Q, n_s,tau_C, sigma_8}. After marginalizing over the other cosmic and experimental variables, we find the current CMB+LSS+SN1 data gives Omega_{…
We review the recent attempts of unifying inflation with quintessence. It appears natural to join the two ends in the framework of brane world cosmology. The models of quintessential inflation belong to the class of {\it non-oscillatory} models for which the mechanism of conventional reheating does not work. Reheating through gravitational particle production is inefficient and leads to the excessive production of relic gravity waves which results in the violation of nucleosynthesis constraint. The mechanism of {\it instant preheating} is quite efficient and is suitable for brane world quintes…
The simplest explanation for early time acceleration (inflation) and the late time acceleration indicated by recent data is that they have a common origin. We investigate another generic cosmological implication of this possiblity, that the baryon asymmetry of the universe may be generated in such models. We identify several novel features of baryogenesis in such a universe, in which a rolling scalar field is always part of the cosmological energy budget. We also propose a concrete mechanism by which the baryon asymmetry of the universe may be generated in this context. We analyze the generic …
A field theory is developed based on the idea that the effective action of yet unknown fundamental theory, at energy scale below M_{p} has the form of expansion in two measures: S=\intd^{4}x[ΦL_{1}+\sqrt{-g}L_{2}] where the new measure Φis defined using the third-rank antisymmetric tensor. In the new variables (Einstein frame) all equations of motion take canonical GR form and therefore models are free of the well-known "defects" that distinguish the Brans-Dicke type theories from GR. All novelty is revealed only in an unusual structure of the effective potential U(ϕ) and interactions which tu…
In continuation of the papers hep-th/0505012 and hep-th/0508101 we investigate the consequences when $N$ open-string tachyons roll down simultaneously. We demonstrate that the $N$-Tachyon system coupled to gravity does indeed give rise to the assisted slow-roll inflation.
We first investigate the attractor solution associated with Assisted Inflation in Heterotic M-Theory to see if it is stable. By perturbing the solutions we find a solitary stable fixed point with the general path through phase space dependent upon the Calabi-Yau data and the number of five-branes. We then go on to examine the effect of including non-perturbative corrections to the inflaton potential arising from boundary-brane instantons as well as higher order brane interaction terms. The result is that Assisted Inflation is only possible if we allow fine tuning of the superpotential, and tha…
We explore within the context of brane cosmology whether it is possible to obtain both early inflation and accelerated expansion during the present epoch through the dynamics of the same scalar field in an exponential potential. Considerations from successful inflation and viable radiation and matter dominated eras impose constraints on the parameters of the potential. We find that the additional requirement of late time quintessence behaviour in conformity with present observations necessitates the inclusion of two exponential terms in the potential.
We consider conditions necessary for a successful implementation of so-called assisted inflation. We generalize the applicability of assisted inflation beyond exponential potentials as originally proposed to include standard chaotic (λϕ^4 or m^2 ϕ^2) models as well. We also demonstrate that in a purely 4-dimensional theory, unless the assisted sector is in fact decoupled, the additional fields of the assisted sector actually impede inflation. As a specific example of an assisted sector, we consider a 5-dimensional KK model for which the extra dimension may be somewhat or much larger than the i…
We obtain a new class of exact cosmological solutions for multi-scalar fields with exponential potentials. We generalize the assisted inflation solutions previously obtained, and demonstrate how they are modified when there exist cross-couplings between the fields, such as occur in supergravity inspired cosmological models.
We present a new approach to quintessential inflation, in which both dark energy and inflation are explained by the evolution of a single scalar field. We start from a simple scalar potential with both oscillatory and exponential behavior. We employ the conventional reheating mechanism of new inflation, in which the scalar decays to light fermions with a decay width that is proportional to the scalar mass. Because our scalar mass is proportional to the Hubble rate, this gives adequate reheating at early times while shutting off at late times to preserve quintessence and satisfy nucleosynthesis…
We extend the idea of assisted inflation to the case of power-law potentials and demonstrate the simultaneous resolution of two major problems that plague chaotic inflation. The implementation of the same idea in the framework of a 5-dimensional, scalar field theory leads to a model of chaotic inflation free of fine-tuning.
We investigate the dynamics of the recently proposed model of assisted inflation. In this model an arbitrary number of scalar fields with exponential potentials evolve towards an inflationary scaling solution, even if each of the individual potentials is too steep to support inflation on its own. By choosing an appropriate rotation in field space we can write down explicitly the potential for the weighted mean field along the scaling solution and for fields orthogonal to it. This demonstrates that the potential has a global minimum along the scaling solution. We show that the potential close t…
We address the problem of the large initial field values in chaotic inflation and propose a remedy in the framework of the so-called assisted inflation. We demonstrate that a 4-dimensional theory of multiple, scalar fields with initial field values considerably below the Planck scale, can give rise to inflation even though none of the individual scalar fields are capable of driving inflation. The problems arising from the presence of possible non-renormalizable interactions is therefore removed. As a concrete example of a theory with multiple scalar fields, we consider a (4+d)-dimensional fiel…
On compactification from higher dimensions, a single free massive scalar field gives rise to a set of effective four-dimensional scalar fields, each with a different mass. These can cooperate to drive a period of inflation known as assisted inflation. We analyze the dynamics of the simplest implementation of this idea, paying particular attention to the decoupling of fields from the slow-roll regime as inflation proceeds. Unlike normal models of inflation, the dynamics does not become independent of the initial conditions at late times. In particular, we estimate the density perturbations obta…
We present a model of inflation based on a racetrack model without flux stabilization. The initial conditions are set automatically through topological inflation. This ensures that the dilaton is not swept to weak coupling through either thermal effects or fast roll. Including the effect of non-dilaton fields we find that moduli provide natural candidates for the inflaton. The resulting potential generates slow-roll inflation without the need to fine tune parameters. The energy scale of inflation must be near the GUT scale and the scalar density perturbation generated has a spectrum consistent…
We investigate the dynamical properties of a class of spatially homogeneous and isotropic cosmological models containing a barotropic perfect fluid and multiple scalar fields with independent exponential potentials. We show that the assisted inflationary scaling solution is the global late-time attractor for the parameter values for which the model is inflationary, even when curvature and barotropic matter are included. For all other parameter values the multi-field curvature scaling solution is the global late-time attractor (in these solutions asymptotically the curvature is not dynamically …
We propose a scenario for inflation based upon the braneworld picture, in which high-energy corrections to the Friedmann equation permit inflation to take place with potentials ordinarily too steep to sustain it. Inflation ends when the braneworld corrections begin to lose their dominance. Reheating may naturally be brought about via gravitational particle production, rather than the usual inflaton decay mechanism; the reheat temperature may be low enough to satisfy the gravitino bound and the Universe becomes radiation dominated early enough for nucleosynthesis. We illustrate the idea by cons…
In inflationary scenarios with more than one scalar field, inflation may proceed even if each of the individual fields has a potential too steep for that field to sustain inflation on its own. We show that scalar fields with exponential potentials evolve so as to act cooperatively to assist inflation, by finding solutions in which the energy densities of the different scalar fields evolve in fixed proportion. Such scaling solutions exist for an arbitrary number of scalar fields, with different slopes for the exponential potentials, and we show that these solutions are the unique late-time attr…
We explore the possibility of obtaining inflation in weakly coupled heterotic string theory, where the model dependent axions are responsible for driving inflation. This model can be considered as a certain extrapolation of $m^{2}ϕ^{2}$-inflation, and is an attempt to explicitly realize the so called N-flation proposal in string theory. The instanton generated potential for the axions essentially has two parameters; a natural mass scale $M$ and the string coupling $g_{s}$. For isotropic compactifications leading to of order $\mathcal{O} (10^4)$ axions in the four dimensional spectrum we find t…
In this paper we propose a new mechanism of inflating the Universe with non-BPS $D4$ branes which decay into stable $D3$ branes via tachyon condensation. In a single brane scenario the tachyon potential is very steep and unable to support inflation. However if the universe lives in a stack of branes produced by a set of non-interacting unstable $\tilde {D4}$ branes, then the associated set of tachyons may drive inflation along our 3 spatial dimensions. After tachyon condensation the Universe is imagined to be filled with a set of parallel stable $D3$ branes. We study the scalar density perturb…
We investigate whether the eternal chaotic inflation can be achieved when the weak gravity conjecture is taken into account. We show that even the assisted chaotic inflation with potential $λϕ^4$ or $m^2ϕ^2$ can not be eternal. The effective field theory description for the inflaton field breaks down before inflation reaches the eternal regime. We also find that the total number of e-folds is still bounded by the inflationary entropy for the assisted inflation.
