E-folds Of Inflation Research Articles

Planck constraints on Higgs modulated reheating of renormalization group improved inflation

Within the framework of RG improved inflationary cosmology motivated by asymptotically safe gravity, we study the dynamics of a scalar field which can be interpreted as the Higgs field. The background trajectories of this model can provide sufficient inflationary e-folds and a graceful exit to a radiation dominated phase. We study the possibility of generating primordial curvature perturbations through the Standard Model Higgs boson. This can be achieved under finely tuned parameter choices by making use of the modulated reheating mechanism. The primordial non-gaussianity is expected to be sizable in this model. Though tightly constrained by the newly released Planck CMB data, this model provides a potentially interesting connection between collider and early universe physics.

Duration of inflation and conditions at the bounce as a prediction of effective isotropic loop quantum cosmology

Loop quantum cosmology with a scalar field is known to be closely linked with an inflationary phase. In this article, we study probabilistic predictions for the duration of slow-roll inflation, by assuming a minimalist massive scalar field as the main content of the universe. The phase of the field in its "prebounce" oscillatory state is taken as a natural random parameter. We find that the probability for a given number of inflationary e-folds is quite sharply peaked around 145, which is consistent with the most favored minimum values. In this precise sense, a satisfactory inflation is therefore a clear prediction of loop gravity. In addition, we derive an original and stringent upper limit on the Barbero-Immirzi parameter. The general picture of inflation, superinflation, deflation, and superdeflation is also much clarified in the framework of bouncing cosmologies.

A non-Gaussian landscape

Primordial perturbations with wavelengths greater thanthe observable universe shift the effective background fields in ourobservable patch from their global averages over the inflatingspace. This leads to a landscape picture where the properties of ourobservable patch depend on its location and may significantly differfrom the expectation values predicted by the underlying fundamentalinflationary model. We show that if multiple fields are presentduring inflation, this may happen even if our horizon exit would bepreceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting|fNL0| >> 10 over the entire inflating volume can have aprobability up to a few tens of percent to generate a non-detectablebispectrum in our observable patch |fNLobs.|≲10.In this work we establish systematic connections between theobservable local properties of primordial perturbations and theglobal properties of the inflating space which reflect theunderlying high energy physics. We study in detail the implicationsof both a detection and non-detection of primordial non-Gaussianityby Planck, and discover novel ways of characterising the naturalnessof different observational configurations.

Explosive particle production in non-commutative inflation

We consider a model of inflation which has recently been proposed in the literature and where inflation is induced by corrections to the energy density coming from the non-commutativity of spacetime. We show that the very rapid inflationary expansion typical of this model is responsible for a burst of particle production which ends inflation and leads to a radiation-dominated phase. We analytically estimate the energy density of these particles and we confront the results with more precise numerical calculations. We estimate the number of inflationary e-folds before the back-reaction of the radiation energy density overcomes the non-commutative effects and terminate inflation naturally.

Weyl invariance and the conductivity of the protoinflationary plasma

We consider a globally neutral Lorentzian plasma as a possible remnant of a preinflationary stage of expansion and pose the problem of the suitable initial conditions for the evolution of the large-scale electromagnetic inhomogeneities. During the protoinflationary regime, the Weyl invariance of the Ohmic current guarantees that the comoving conductivity is approximately constant. The subsequent breaking of Weyl invariance by the masses of the charge carriers drives the conductivity to zero. The newly derived conducting initial conditions for the amplification of large-scale magnetic fields are contrasted with the conventional vacuum initial conditions. It is shown, in a specific class of examples, that when the number of inflationary e-folds is close to minimal, the effects of the conducting initial conditions cannot be neglected.

The inflating curvaton

The primordial curvature perturbation ζ may be generated by some curvaton field σ, which is negligible during inflation and has more or less negligible interactions until it decays. In the current scenario, the curvaton starts to oscillate while its energy density ρσ is negligible. We explore the opposite scenario, in which ρσ drives a few e-folds of inflation before the oscillation begins. In this scenario for generating ζ it is exceptionally easy to solve the η problem; one just has to make the curvaton a string axion, with anomaly-mediated susy breaking which may soon be tested at the LHC. The observed spectral index n can be obtained with a potential V∝ϕp for the first inflation; p = 1 or 2 is allowed by the current uncertainty in n but the improvement in accuracy promised by Planck may rule out p = 1. The predictions include (i) running n′ ≃ 0.0026 (0.0013) for p = 1 (2) that will probably be observed, (ii) non-gaussianity parameter fNL; ∼ −1 that may be observed, (iii) tensor fraction r is probably too small to ever observed.

A meandering inflaton

If the cosmological inflationary scenario took place in the cosmic landscape in string theory, the inflaton, the scalar mode responsible for inflation, would have meandered in a complicated multi-dimensional potential. We show that this meandering property naturally leads to many e-folds of inflation, a necessary condition for a successful inflationary scenario. This behavior also leads to fluctuations in the primordial power spectrum of the cosmic microwave background radiation, which may be detected in a near future cosmic variance limited experiment like PLANCK.

Replication regulates volume weighting in quantum cosmology

Probabilities for observations in cosmology are conditioned both on the Universe's quantum state and on local data specifying the observational situation. We show the quantum state defines a measure for prediction through such conditional probabilities that is well-behaved for spatially large or infinite universes when the probabilities that our data are replicated are taken into account. In histories where our data are rare volume weighting connects top-down probabilities conditioned on both the data and the quantum state to the bottom-up probabilities conditioned on the quantum state alone. We apply these principles to a calculation of the number of inflationary e-folds in a homogeneous, isotropic minisuperspace model with a single scalar field moving in a quadratic potential. We find that volume weighting is justified and the top-down probabilities favor a large number of e-folds, hereby predicting the curvature of our Universe at the present time to be approximately zero.

Measure problem in cosmology

The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a ``magnetic flux'' of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat Friedmann-Lemaitre-Robertson-Walker universes. We show that the divergence is removed if we identify universes which are so flat they cannot be observationally distinguished. The resulting measure is independent of time and of the choice of coordinates on the space of fields. We further show that, for some quantities of interest, the measure is very insensitive to the details of how the identification is made. One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for $N$ e-folds of inflation in single-field, slow-roll models is suppressed by of order $\mathrm{exp}(\ensuremath{-}3N)$ and we discuss the implications of this result.

Effects of inflation on a cosmic string loop population

We study the evolution of simple cosmic string loop solutions in an inflationary universe. We show, for the particular case of circular loops, that periodic solutions do exist in a de Sitter universe, below a critical loop radius R{sub c}H=1/2. On the other hand, larger loops freeze in comoving coordinates, and we explicitly show that they can survive more e-foldings of inflation than pointlike objects. We discuss the implications of these findings for the survival of realistic cosmic string loops during inflation and for the general characteristics of post-inflationary cosmic string networks. We also consider the analogous solutions for domain walls, in which case the critical radius is R{sub c}H=2/3.

New constraints on the observable inflaton potential from WMAP and SDSS

We derive some new constraints on single-field inflation from the Wilkinson Microwave Anisotropy Probe 3-year data combined with the Sloan Luminous Red Galaxy survey. Our work differs from previous analyses by focusing only on the observable part of the inflaton potential, or in other words, by making absolutely no assumption about extrapolation of the potential from its observable region to its minimum (i.e., about the branch of the potential responsible for the last {approx}50 inflationary e-folds). We only assume that inflation starts at least a few e-folds before the observable Universe leaves the Hubble radius, and that the inflaton rolls down a monotonic and regular potential, with no sharp features or phase transitions. We Taylor-expand the inflaton potential at order v=2, 3 or 4 in the vicinity of the pivot scale, compute the primordial spectra of scalar and tensor perturbations numerically and fit the data. For v>2, a large fraction of the allowed models is found to produce a large negative running of the scalar tilt, and to fall in a region of parameter space where the second-order slow-roll formalism is strongly inaccurate. We release a code for the computation of inflationary perturbations which is compatible with cosmomc.

Observational consequences of a landscape

In this paper we consider the implications of the "landscape" paradigm for the large scale properties of the universe. The most direct implication of a rich landscape is that our local universe was born in a tunnelling event from a neighboring vacuum. This would imply that we live in an open FRW universe with negative spatial curvature. We argue that the "overshoot" problem, which in other settings would make it difficult to achieve slow roll inflation, actually favors such a cosmology. We consider anthropic bounds on the value of the curvature and on the parameters of inflation. When supplemented by statistical arguments these bounds suggest that the number of inflationary efolds is not very much larger than the observed lower bound. Although not statistically favored, the likelihood that the number of efolds is close to the bound set by observations is not negligible. The possible signatures of such a low number of efolds are briefly described.

Langevin analysis of eternal inflation

It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill, thereby continually revitalizing the inflationary process in some regions. In this paper we investigate a simple model of this process, pertaining to inflation with a quartic potential, in which analytic progress may be made. We calculate several quantities of interest, such as the expected number of inflationary efolds, first without and then with various selection effects. With no additional weighting, the stochastic noise has little impact on the total number of inflationary efoldings even if the inflaton starts with a Planckian energy density. A "rolling" volume factor, i.e. weighting in proportion to the volume at that time, also leads to a monotonically decreasing Hubble constant and hence no eternal inflation. We show how stronger selection effects including a constraint on the initial and final states and weighting with the final volume factor can lead to a picture similar to that usually associated with eternal inflation.

On the stability of the anomaly-induced inflation

We analyze various phases of inflation based on the anomaly-induced effective action of gravity (modified Starobinsky model), taking the cosmological constant Λ and k=0,±1 topologies into account. The total number of the inflationary e-folds may be enormous, but at the last 65 of them the inflation greatly slows down due to the contributions of the massive particles. For the supersymmetric particle content, the stability of inflation holds from the initial point at the sub-Planck scale until the supersymmetry breaks down. After that the universe enters into the unstable regime with the eventual transition into the stable FRW-like evolution with small positive cosmological constant. It is remarkable, that all this follows automatically, without fine-tuning of any sort, independent on the values of Λ and k. Finally, we consider the stability under the metric perturbations during the last 65 e-folds of inflation and find that the amplitude of the ones with the wavenumber below a certain cutoff has an acceptable range.

Cosmological Density Perturbations from a Quantum Gravitational Model of Inflation

We derive the implications for anisotropies in the cosmic microwave background following from a model of inflation in which a bare cosmological constant is gradually screened by an infrared process in quantum gravity. The model predicts that the amplitude of scalar perturbations is $A_S = (2.0 \pm .2) \times 10^{-5}$, that the tensor-to-scalar ratio is $r \approx 1.7 \times 10^{-3}$, and that the scalar and tensor spectral indices are $n \approx .97$ and $n_T \approx -2.8 \times 10^{-4}$, respectively. By comparing the model's power spectrum with the COBE 4-year RMS quadrupole, the mass scale of inflation is determined to be $M = (.72 \pm .03) \times 10^{16}~{\rm GeV}$. At this scale the model produces about $10^8$ e-foldings of inflation, so another prediction is $\Omega = 1$.

Quantum origin of the early inflationary universe

We give a detailed presentation of a recently proposed mechanism of generating the energy scale of inflation by loop effects in quantum cosmology. We discuss the quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states and present a universal effective action algorithm for the distribution function of chaotic inflationary cosmologies in both of these states. The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling mode] driven by the inflaton field with large negative constant ξ of non-minimal interaction. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant H ≃ 10 −5 m p, its quantum width ΔH H ≃ 10 −5 and the number of inflationary e-foldings N ⩾ 60) are found to be in good correspondence with the observational status of inflation theory, provided the coupling constants of the theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle physics model.

QUANTUM ORIGIN OF THE ENERGY SCALE OF INFLATION: NO-BOUNDARY VS TUNNELLING WAVEFUNCTIONS

Quantum origin of the early inflationary Universe from the no-boundary and tunnelling quantum states is considered in the one-loop approximation of quantum cosmology. A universal effective action algorithm for the distribution function of chaotic inflationary cosmologies is derived for both of these states. The energy scale of inflation is calculated by finding a sharp probability peak in this distribution function for a tunnelling model driven by the inflaton field with large negative constant ξ of nonminimal interaction. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant H≃10−5mp, its quantum width ΔH/H≃10−5 and the number of inflationary e-foldings N≃60) are found to be in good correspondence with the observational status of inflation theory, provided the coupling constants of the theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle physics model.

INFLATION FROM SUPERSTRINGS

We investigate the possibility of obtaining inflationary solutions from a low energy Lagrangian coming from superstrings. In any viable scheme, the dilaton and the moduli fields have to be stabilized and before this happens, no other field may be used as the inflaton. We show that in a class of models where supersymmetry breaking occurs via gaugino condensation, the dilaton and the moduli fields can be stabilised in a way that enables the use of chiral matter fields in order to obtain enough e-folds of inflation. In a superstring model this is not straightforward, because the form of the Kähler potential is restricted and certain relations between the chiral and moduli fields lead in general to a steep potential. We identify a subclass of Kähler potentials and a certain region of the parameter space of the chiral and moduli fields that may lead to enough inflation. The conditions that we have derived for inflation due to chiral fields are generic and apply also in schemes where the dilaton and moduli fields may be frozen in alternative ways. Demanding that the potential terms associated with the chiral fields do not spoil the dilaton and moduli minimization under the specific scheme that we use to freeze the dilaton, leads to severe constraints on the magnitude of the density fluctuations.

Quantum scale of inflation and particle physics of the early universe

The quantum gravitational scale of inflation is calculated by finding a sharp probability peak in the distribution function of chaotic inflationary cosmologies driven by a scalar field with large negative constant Ξ of nonminimal interaction. In the case of the no-boundary state of the universe this peak corresponds to the eternal inflation, while for the tunnelling quantum state it generates a standard inflationary scenario. The sub-Planckian parameters of this peak (the mean value of the corresponding Hubble constant H ≅ 10 −5mp , its quantum width Δ H H ≅ 10 −5 and the number of inflationary e-foldings N ≅ 60 ) are found to be in good correspondence with the observational status of inflation theory, provided the coupling constants of the theory are constrained by a condition which is likely to be enforced by the (quasi) supersymmetric nature of the sub-Planckian particle physics model.