An earlier paper points out that a quantum treatment of the string landscape is necessary. It suggests that the wavefunction of the universe is mobile in the landscape until the universe reaches a meta-stable site with its cosmological constant $Λ_0$ smaller than the critical value $Λ_c$, where $Λ_c$ is estimated to be exponentially small compared to the Planck scale. Since this site has an exponentially long lifetime, it may well be today's universe. We investigate specific scenarios based on this quantum diffusion property of the cosmic landscape and find a plausible scenario for the early universe. In the last fast tunneling to the $Λ_0$ ($<Λ_c$) site in this scenario, all energies are stored in the nucleation bubble walls, which are released to radiation only after bubble collisions and thermalization. So the $Λ_0$ site is chosen even if $Λ_0$ plus radiation is larger than $Λ_c$, as long as the radiation does not destabilize the $Λ_0$ vacuum. A consequence is that inflation must happen before this last fast tunneling, so the inflationary scenario that emerges naturally is extended brane inflation, where the brane motion includes a combination of rolling, fast tunnelings, slow-roll, hopping and percolation in the landscape. We point out that, in the brane world, radiation during nucleosynthesis are mostly on the standard model branes (brane radiation, as opposed to radiation in the bulk). This distinction may lead to interesting dynamics. We consider this paper as a road map for future investigations.
We study some aspects of fine tuning in inflationary scenarios within string theory flux compactifications and, in particular, in models of accidental inflation. We investigate the possibility that the apparent fine-tuning of the low energy parameters of the theory needed to have inflation can be generically obtained by scanning the values of the fluxes over the landscape. Furthermore, we find that the existence of a landscape of eternal inflation in this model provides us with a natural theory of initial conditions for the inflationary period in our vacuum. We demonstrate how these two effect…
We determine the frequency of regions of small-field inflation in the Wigner landscape as an approximation to random supergravities/type IIB flux compactifications. We show that small-field inflation occurs exponentially more often than large-field inflation The power of primordial gravitational waves from inflation is generically tied to the scale of inflation. For small-field models this is below observational reach. However, we find small-field inflation to be dominated by the highest inflationary energy scales compatible with a sub-Planckian field range. Hence, we expect a typical tensor-t…
We investigate slow-roll inflation in a multi-field random Gaussian landscape. The landscape is assumed to be small-field, with a correlation length much smaller than the Planck scale. Inflation then typically occurs in small patches of the landscape, localized near inflection or saddle points. We find that the inflationary track is typically close to a straight line in the field space, and the statistical properties of inflation are similar to those in a one-dimensional landscape. This picture of multi-field inflation is rather different from that suggested by the Dyson Brownian motion model;…
We recapitulate multiple arguments that Eternal Inflation, and the String Landscape are actually part of the Swampland: ideas in Effective Quantum Field Theory that do not have a counterpart in genuine models of Quantum Gravity.
We show that GUT cosmic strings generically form after inflation if a {\it non-inert} symmetry breaks after inflation; they form irrespectively of the inflationary scenario and in both supersymmetric and non-supersymmetric theories.
In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, $P \sim 10^{-3}$.
We investigate the validity of the assertion that eternal inflation populates the landscape of string theory. We verify that bubble solutions do not satisfy the Klein Gordon equation for the landscape potential. Solutions to the landscape potential within the formalism of quantum cosmology are Anderson localized wavefunctions. Those are inconsistent with inflating bubble solutions. The physical reasons behind the failure of a relation between eternal inflation and the landscape are rooted in quantum phenomena such as interference between wavefunction concentrated around the various vacua in th…
We briefly survey our present understanding of the string landscape, and use it to discuss the chances that we will see low energy supersymmetry at the LHC.
I review some aspects of obtaining inflation from string theory, in particular brane-antibrane inflation within the framework of KKLMMT, and racetrack inflation. Further, I discuss recent work on the problem of reheating after brane-antibrane annihilation, and possible distinctive features of production of cosmic string and brane defects at this time.
We consider the coupling of racetrack inflation to matter fields as realised in the D3/D7 brane system. In particular, we investigate the possibility of cosmic string formation in this system. We find that string formation before or at the onset of racetrack inflation is possible, but they are then inflated away. Furthermore, string formation at the end of inflation is prevented by the presence of the moduli sector. As a consequence, no strings survive racetrack inflation.
The much-discussed swampland conjectures suggest significant constraints on the properties of string theory landscape and on the nature of the multiverse that this landscape can support. The conjectures are especially constraining for models of inflation; in particular, they exclude the existence of de Sitter (dS) vacua. If the conjectures are false and dS vacua do exist, it still appears that their construction in string theory requires a fair amount of fine-tuning, so they may be vastly outnumbered by AdS vacua. Here we explore the multiverse structure suggested by these considerations. We c…
We investigate inflation in a multi-dimensional landscape with a hierarchy of energy scales, motivated by the string theory, where the energy scale of Kahler moduli is usually assumed to be much lower than that of complex structure moduli and dilaton field. We argue that in such a landscape, the dynamics of slow-roll inflation is governed by the low-energy potential, while the initial condition for inflation are determined by tunneling through high-energy barriers. We then use the scale factor cutoff measure to calculate the probability distribution for the number of inflationary e-folds and t…
We demonstrate an inflationary solution to the cosmological horizon problem during the Hagedorn regime in the early universe. Here the observable universe is confined to three spatial dimensions (a three-brane) embedded in higher dimensions. The only ingredients required are open strings on D-branes at temperatures close to the string scale. No potential is required. Winding modes of the strings provide a negative pressure that can drive inflation of our observable universe. Hence the mere existence of open strings on branes in the early hot phase of the universe drives Hagedorn inflation, whi…
Inflation is now a basic ingredient of the modern cosmology. After reviewing the basic characteristics of inflation, we briefly discuss inflation in string and brane theories, focusing on the problem of the exit from inflation in these theories. We present a model, based on type-0 string theory, in which our universe after the inflationary phase, passes smoothly to a flat Robertson-Walker universe.
In this article we will overview several aspects of the string landscape, namely intersecting D-brane models and their statistics, possible model independent LHC signatures of intersecting brane models, flux compactification, moduli stabilization in type II compactifications, domain wall solutions and brane inflation.
Recently we introduced an inflationary setup in which the inflaton fields are matrix valued scalar fields with a generic quartic potential, M-flation. In this work we study the landscape of various inflationary models arising from M-flation. The landscape of the inflationary potential arises from the dynamics of concentric multiple branes in appropriate flux compactifications of string theory. After discussing the classical landscape of the theory we study the possibility of transition among various inflationary models appearing at different points on the landscape, mapping the quantum landsca…
We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations $n_s$ and its running $α_s$. These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field…
Multi-Stage and Multi-Field Inflation in Random Inflationary Landscapes
Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Laboratoire de Physique de l’École Normale Supérieure, ENS, CNRS, Université PSL, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，ENS，CNRS，PSL大学，索邦大学，巴黎西岱大学）；Tsinghua University（清华大学）
We investigate the nucleation of circular cosmic strings in models of generalized inflationary universes with an accelerating scale factor. We consider toy cosmological models of a smooth inflationary exit and transition into a flat Minkowski spacetime. Our results establish that an inflationary expanding phase is necessary but not sufficient for quantum nucleation of circular cosmic strings to occur.
In this paper we present an initial exploration of the Calabi-Yau landscape in the context of Kahler moduli inflation. We review how the slow-roll requirement on the scalar potential translates to a geometric constraint on the Kahler geometry of the vacuum. This constraint leads to a hard bound on the moduli space geometry and we consider the effects of this constraint on the string landscape that arises in type IIB string compactifications on an O3/O7 orientifold. Most notably we find that the inflationary constraint is independent of the moduli space dimension and only 6.57% of geometries in…
We conjecture that the inflation models with trans-Planckian excursions in the field space should be in the swampland. We check this conjecture in a few examples and investigate the constraints on the spectral index for the slow-roll inflation model in string landscape where the variation of inflaton during the period of inflation is less than the Planck scale $M_p$. A red primordial power spectrum with a lower bound on the spectral index is preferred. Both the tensor-scalar ratio and the running can be ignored.
We study the possibility of extended inflation in the effective theory of gravity from strings compactified to four dimensions and find that it strongly depends on the mechanism of supersymmetry breaking. We consider a general class of string--inspired models which are good candidates for successful extended inflation. In particular, the $ω$--problem of ordinary extended inflation is automatically solved by the production of only very small bubbles until the end of inflation. We find that the inflaton field could belong either to the untwisted or to the twisted massless sectors of the string s…
Recent developments in string theory suggest that string theory landscape of vacua is vast. It is natural to ask if this landscape is as vast as allowed by consistent-looking effective field theories. We use universality ideas from string theory to suggest that this is not the case, and that the landscape is surrounded by an even more vast swampland of consistent-looking semiclassical effective field theories, which are actually inconsistent. Identification of the boundary of the landscape is a central question which is at the heart of the meaning of universality properties of consistent quant…
In light of recent discussions of the string landscape, it is essential to understand the degree to which string theory is predictive. We argue that it is unlikely that the landscape as a whole will exhibit unique correlations amongst low-energy observables, but rather that different regions of the landscape will exhibit different overlapping sets of correlations. We then provide a statistical method for quantifying this degree of predictivity, and for extracting statistical information concerning the relative sizes and overlaps of the regions corresponding to these different correlation class…
The effect of fluxes on open string moduli is studied by analyzing the constraints imposed by supersymmetry on D-branes in type IIB flux backgrounds. We show that generically the conditions of supersymmetry cannot be maintained when moving along the geometrical moduli space of the brane, so that open string moduli are lifted. We argue that there is a disconnected and discrete set of supersymmetric solutions to the open string equations of motion, which extends the familiar closed string landscape to the open string sector.
We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function…
An anthropic understanding of the cosmological constant requires that the vacuum energy at late time scans from one patch of the universe to another. If the vacuum energy during inflation also scans, the various patches of the universe acquire exponentially differing volumes. In a generic landscape with slow-roll inflation, we find that this gives a steeply varying probability distribution for the normalization of the primordial density perturbations, resulting in an exponentially small fraction of observers measuring the COBE value of 10^-5. Inflationary landscapes should avoid this "σproblem…
In this lecture I make some educated guesses, about the landscape of string theory vacua. Based on the recent work of a number of authors, it seems plausible that the lanscape is unimaginably large and diverse. Whether we like it or not, this is the kind of behavior that gives credence to the Anthropic Principle. I discuss the theoretical and conceptual issues that arise in developing a cosmology based on the diversity of environments implicit in string theory.
The D3/D7 inflation is studied in the framework of Type 0B string theory. Due to the presence of the closed string tachyon, the constant gauge field flux on the transverse worldvolume of D7-brane is almost arbitrary in having an attractive inflaton potential energy. Besides, a positive cosmological constant appears in this model whose magnitude is related to the volume modulus of the D7-brane transverse worldvolume.
Motivated by the string landscape, inflation may happen on a high dimensional complicated potential. We propose a new way to construct some high dimensional random potentials, and study inflation on top of that, for up to 50-dimensions in field space. Especially, random bifurcations of classical inflationary trajectory are studied. It is shown that the bifurcation probability increases as a function of number of dimensions. Those random bifurcations are not consistent with observations, and dramatically limit the parameter space of inflation on a complicated landscape. For example, in 10 dimen…
We investigate the possibility that spiral inflation can be realized using the near-conifold flux potentials for the complex structure moduli in type IIB string theory compactified on a Calabi-Yau manifold. Using the explicit form of the flux potential for complex structure moduli, we provide analytical and numerical arguments showing that spiral inflation is difficult to support. We also show that for this sector of low energy string theories, a viable spiral inflationary scenario would owe its success to a de Sitter-like vacuum energy, with minimal reliance on the non-gradient flow field tra…
In this paper we describe ideas about the string landscape, and how to relate it to the physics of the Standard Model of particle physics. First, we give a short status report about heterotic string compactifications. Then we focus on the statistics of D-brane models, on the problem of moduli stabilization, and finally on some attempts to derive a probability wave function in moduli space, which goes beyond the purely statistical count of string vacua.
This article is the author's PhD thesis. After a review of string vacua obtained through compactification (with and wothout fluxes), it presents and describes various aspects of the Landscape of string vacua. At first it gives an introduction and an overview of the statistical study of the set of four dimensional string vacua, giving the detailed study of one corner of this set (G2-holonomy compactifications of M-theory). Then it presents the ten dimensional approach to string vacua, concentrating on the ten dimensional description of the Type IIA flux vacua. Finally it gives two examples of m…
Chain inflation takes place in the string theory landscape as the universe tunnels rapidly through a series of ever lower energy vacua such as may be characterized by quantized changes in four form fluxes. The string landscape may be well suited to an early period of rapid tunneling, as required by chain inflation, followed by a later period of slow tunneling, such as may be required to explain today's dark energy and small cosmological constant. Each tunneling event (which can alternatively be thought of as a nucleation of branes) provides a fraction of an e-folding of inflation, so that hund…
The most naive interpretation of the BICEP2 data is the chaotic inflation by an inflaton with a quadratic potential. When combined with supersymmetry, we argue that the inflaton plays the role of right-handed scalar neutrino based on rather general considerations. The framework suggests that the right-handed sneutrino tunneled from a false vacuum in a landscape to our vacuum with a small negative curvature and suppressed scalar perturbations at large scales.
We consider a string inspired effective Lagrangian for the graviton and dilaton, containing Einstein gravity at the zero slope limit. The numerical solution of the problem shows asymptotically an inflationary universe. The time is measured by the dilaton, as one expects. The result is independent of the introduction of ad-hoc self interactions for the dilaton field.
We construct a multi-field inflationary model consisting of multiple Kähler moduli derived from type IIB string compactification in the large volume limit. The model consists of both heavy and light fields, with the former being frozen during the inflationary period and the latter acting as the inflaton(s). We study the evolution of all the fields during and after inflation until the preheating era when all the fields oscillate around their vacuum expectation values. Our numerical analysis shows that the curvature perturbations have an almost scale invariant power spectrum with $n_s \simeq 0.9…
We consider inflation driven near a saddle point in a higher dimensional field space, which is the most likely type of slow roll inflation on the string theoretical landscape; anthropic arguments need to be invoked in order to find a sufficiently flat region. To give all inflatons large masses after inflation and yield a small but positive cosmological constant, the trajectory in field space needs to terminate in a hole on the inflationary plateau, introducing a curved end-of-inflation hypersurface. We compute non-Gaussianities (bi- and tri-spectrum) caused by this curved hyper-surface and fin…
I examine some non-anthropic approaches to the string landscape. These approaches are based on finding the initial conditions of the universe using the wavefunction of the multiverse to select the most probable vacuum out of this landscape. All approaches tackled so far seems to have their own problems and there is no clear cut alternative to anthropic reasoning. I suggest that finding the initial conditions may be irrelevant since all possible vacua on the landscape are possible initial state conditions and eternal inflation could generate all the other vacua. We are now left to reason out wh…
Multiple axions form a landscape in the presence of various shift symmetry breaking terms. Eternal inflation populates the axion landscape, continuously creating new universes by bubble nucleation. Slow-roll inflation takes place after the tunneling event, if a very flat direction with a super-Planckian decay constant arises due to the alignment mechanism. We study the vacuum structure as well as possible inflationary dynamics in the axion landscape scenario, and find that the inflaton dynamics is given by either natural or multi-natural inflation. In the limit of large decay constant, it is a…
We consider the motion of the brane universe moving in a background bulk space of tachyonic and non-tachyonic type 0B string theory. The effective densities are calculated for both cases and they show different power law behavior. Brane inflation for non-tachyonic type 0B background has the same power law behavior as that for type IIB background. The brane inflation under tachyonic background is less divergent than the one without tachyon. The role of tachyonic field in brane inflation scenario is different from that of the ordinary matter field.
We numerically generate the six-dimensional landscape of D3-brane inflation and identify patches of eternal inflation near sufficiently flat inflection points of the potential. We show that reasonable measures that select patches of eternal inflation in the landscape yield sharp predictions for the spectral properties of primordial perturbations on observable scales. These include a scalar tilt of .936, a running of the scalar tilt -.00103, undetectably small tensors and non-Gaussianity, and no observable spatial curvature. Our results explicitly demonstrate that precision cosmology probes the…
We study the problem of obtaining de Sitter and inflationary vacua from dimensional reduction of double field theory (DFT) on nongeometric string backgrounds. In this context, we consider a new class of effective potentials that admit Minkowski and de Sitter minima. We then construct a simple model of chaotic inflation arising from T-fold backgrounds and we discuss the possibility of trans-Planckian field range from nongeometric monodromies as well as the conditions required to get slow roll.
The inflationary paradigm provides a robust description of the peculiar initial conditions which are required for the success of the Hot Big Bang model of cosmology, as well as of the recent precision measurements of temperature fluctuations within the cosmic microwave background. Furthermore, the success of this description indicates that inflation is likely to be associated with physics at energies considerably higher than the weak scale, for which string theory is arguably our most promising candidate. These observations strongly motivate a detailed search for inflation within string theory…
Theories of the cosmological constant fall into two classes, those in which the vacuum energy is fixed by the fundamental theory and those in which it is adjustable in some way. For each class we discuss key challenges. The string theory landscape is an example of an adjustment mechanism. We discuss the status of this idea, and future directions.
In the model of Chain Inflation, a sequential chain of coupled scalar fields drives inflation. We consider a multidimensional potential with a large number of bowls, or local minima, separated by energy barriers: inflation takes place as the system tunnels from the highest energy bowl to another bowl of lower energy, and so on until it reaches the zero energy ground state. Such a scenario can be motivated by the many vacua in the stringy landscape, and our model can apply to other multidimensional potentials. The ''graceful exit'' problem of Old Inflation is resolved since reheating is easily …
This short note emphasises a potential tension between string models of inflation based on systems of branes and antibranes and the spectrum of strings in curved space, in particular the requirement that the leading Regge trajectory extends to the Planck scale allowing for the conventional string theory UV completion of gravity.
We consider the conditions needed to unify the description of dark matter, dark energy and inflation in the context of the string landscape. We find that incomplete decay of the inflaton field gives the possibility that a single field is responsible for all three phenomena. By contrast, unifying dark matter and dark energy into a single field, separate from the inflaton, appears rather difficult.
We propose a landscape of many axions, where the axion potential receives various contributions from shift symmetry breaking effects. We show that the existence of the axion with a super-Planckian decay constant is very common in the axion landscape for a wide range of numbers of axions and shift symmetry breaking terms, because of the accidental alignment of axions. The effective inflation model is either natural or multi-natural inflation in the axion landscape, depending on the number of axions and the shift symmetry breaking terms. The tension between BICEP2 and Planck could be due to smal…
We note that there is an exception to the general arguments that no falsifiable predictions can be made, on the basis of of presently available data, by applying the weak anthropic principle (WAP) to the landscape of string theory. If there are infinitely more vacua in the landscape for one sign of a parameter than the other, within an anthropicaly allowed range, then under very weak assumptions about the probability measure one gets a firm prediction favoring that sign of that parameter. It is interesting to note that while the understanding of the string landscape is evolving, present eviden…
We present an orientifold of a toric singularity allowing for a configuration of fractional branes which corresponds to a gauge theory that dynamically breaks supersymmetry in a stable vacuum. This model represents the first such instance within the gauge/gravity duality.
There are hidden observables for inflation, such as features localized in position space, which do not manifest themselves when only one inflation trajectory is considered. To address this issue, we investigate inflation dynamics in a landscape mimicked by a random potential. We calculate the probability for bifurcation of the inflation trajectory in multi-stream inflation. Depending on the shape of the random bumps and the distance between bumps in the potential, there is a phase transition: on one side of the critical curve in parameter space isocurvature fluctuation are exponentially amplif…
Motivated by the string landscape we examine scenarios for which inflation is a two-step process, with a comparatively short inflationary epoch near the string scale and a longer period at a much lower energy (like the TeV scale). We quantify the number of $e$-foldings of inflation which are required to yield successful inflation within this picture. The constraints are very sensitive to the equation of state during the epoch between the two inflationary periods, as the extra-horizon modes can come back inside the horizon and become reprocessed. We find that the number of $e$-foldings during t…
We model the essential features of eternal inflation on the landscape of a dense discretuum of vacua by the potential $V(ϕ)=V_{0}+δV(ϕ)$, where $|δV(ϕ)|\ll V_{0}$ is random. We find that the diffusion of the distribution function $ρ(ϕ,t)$ of the inflaton expectation value in different Hubble patches may be suppressed due to the effect analogous to the Anderson localization in disordered quantum systems. At $t \to \infty$ only the localized part of the distribution function $ρ(ϕ, t)$ survives which leads to dynamical selection principle on the landscape. The probability to measure any but a sma…
Cosmologists have embraced a particular ad hoc formula for the primordial power spectrum from inflation for universes with $Ω_0 < 1$. However, the so-called ``Open Inflation'' models, which are attracting renewed interest in the context of the ``string theory landscape'' give a different result, and offer a more fully developed picture of the cosmology and fundamental physics basis for inflation with $Ω_0 < 1$. The Open Inflation power spectrum depends not only on $Ω_0$, but on the parameters of the effective fields that drive the universe {\em before} the Big Bang (in ``another part of the la…
The cosmological evolution of the string landscape is expected to consist of multiple stages of old inflation with large cosmological constant ending by tunnelling. Old inflation has a well known graceful exit problem as the observable universe becomes empty, devoid of any entropy. Simultaneously, in the quest for reheating the right degrees of freedom, it is important that the final stage of inflation reheat Standard Model sector. It is known that inflation can occur naturally along a flat direction of the Minimal Supersymmetric Standard Model (MSSM), solving the reheating problem, but the in…
Random, multifield functions can set generic expectations for landscape-style cosmologies. We consider the inflationary implications of a landscape defined by a Gaussian random function, which is perhaps the simplest such scenario. Many key properties of this landscape, including the distribution of saddles as a function of height in the potential, depend only on its dimensionality, $N$, and a single parameter, $γ$, which is set by the power spectrum of the random function. We show that for saddles with a single downhill direction the negative mass term grows smaller, relative to the average m…
The refined de Sitter derivative conjecture provides constraints to potentials that are low energy effective theories of quantum gravity. It can give direct bounds on inflationary scenarios and determine whether the theory is in the Landscape or the Swampland. We consider the `Higgs inflation' scenario taking the refined de Sitter derivative conjecture into account. Obtaining the critical lines for the potential, we find a conjecture parameter space in which the `Higgs inflation' is to be in the Landscape. Comparing with the model independent observational bounds from recent data we find that …
A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by volume, a flat potential for slow-roll inflation is also naturally understood, since the flatter the potential the larger the volume of the sub-universe. However, such inflationary landscapes have a serious problem, predicting an environment that makes it exponentially hard for observers to exist and giving an exponentially small probability for a moderate univer…
We show that the shape of the inflationary landscape potential may be constrained by analyzing cosmological data. The quantum fluctuations of fields orthogonal to the inflationary trajectory may have probed the structure of the local landscape potential, inducing non-Gaussianity (NG) in the primordial distribution of the curvature perturbations responsible for the cosmic microwave background (CMB) anisotropies and our Universe's large-scale structure. The resulting type of NG (tomographic NG) is determined by the shape of the landscape potential, and it cannot be fully characterized by 3- or 4…
