We provide a pedagogical overview of inflation in string theory. Our theme is the sensitivity of inflation to Planck-scale physics, which we argue provides both the primary motivation and the central theoretical challenge for the subject. We illustrate these issues through two case studies of inflationary scenarios in string theory: warped D-brane inflation and axion monodromy inflation. Finally, we indicate how future observations can test scenarios of inflation in string theory.
In this paper we show how the string landscape can be constrained using observational data. We illustrate this idea by focusing on Fibre Inflation which is a promising class of string inflationary models in type IIB flux compactifications. We determine the values of the microscopic flux-dependent parameters which yield the best fit to the most recent cosmological datasets.
We review cosmological inflation and its realization in quantum field theory and in string theory. This material is a portion of a book, also entitled "Inflation and String Theory", to be published by Cambridge University Press.
We describe a simple model of chaotic inflation in supergravity where one can easily tune not only the basic cosmological parameters such as n_{s}, r, and f_NL, but also a possible (subdominant) cosmic string contribution to the CMB anisotropy.
We consider gravitational wave production during inflation in type IIB string theory, and the possibility of observable gravitational waves in small field inflation. We show that the gauge field excitations on a set of coincident D7 branes, itself critical for moduli stabilization and hence intrinsic to inflation in string theory, coupled with axion fields from bulk fluxes, can act as a spectator sector during inflation. This results in a large production of chiral gravitational waves, even for relatively small values of the axion-gauge field coupling. We extend this to include a monodromy for…
We present an overview of inflationary models derived from string theory focusing mostly on closed string moduli as inflatons. After a detailed discussion of the eta-problem and different approaches to address it, we describe possible ways to obtain a de Sitter vacuum with all closed string moduli stabilised. We then look for inflationary directions and present some of the most promising scenarios where the inflatons are either the real or the imaginary part of Kaehler moduli. We pay particular attention on extracting potential observable implications, showing how most of the scenarios predict…
Classical string cosmology consists of two branches related to each other by scale-factor duality: a super-inflation branch and a Friedmann-Robertson-Walker (FRW) branch. Curvature and string coupling singularity separates the two branches, hence posing `graceful exit problem' to super-inflationary string cosmology. In an exactly soluble two-dimensional compactification model it is shown that quantum back reaction retards curvature and string coupling growth and connects the super-inflation branch to the FRW branch without encountering a singularity. This may offer an attractive solution to th…
This is a short review of string cosmology. We wish to connect string-scale physics as closely as possible to observables accessible to current or near-future experiments. Our possible best hope to do so is a description of inflation in string theory. The energy scale of inflation can be as high as that of Grand Unification (GUT). If this is the case, this is the closest we can possibly get in energy scales to string-scale physics. Hence, GUT-scale inflation may be our best candidate phenomenon to preserve traces of string-scale dynamics. Our chance to look for such traces is the primordial gr…
In type IIB Fibre Inflation models the inflaton is a Kaehler modulus which is kinetically coupled to the corresponding axion. In this setup the curvature of the field space induces tachyonic isocurvature perturbations normal to the background inflationary trajectory. However we argue that the associated instability is unphysical since it is due to the use of ill-defined entropy variables. In fact, upon using the correct relative entropy perturbation, we show that in Fibre Inflation axionic isocurvature perturbations decay during inflation and the dynamics is essentially single-field.
We present a single-field string inflationary model which allows for the generation of primordial black holes in the low mass region where they can account for a significant fraction of the dark matter abundance. The potential is typical of type IIB fibre inflation models and features a plateau at CMB scales and a near inflection point at large distance scales where the power spectrum is enhanced due to a period of ultra slow-roll. The tunability of the underlying parameters is guaranteed by scanning through the string landscape and their stability against quantum corrections is ensured by an …
We develop sequestered inflation models, where inflation occurs along flat directions in supergravity models derived from type IIB string theory. It is compactified on a ${\mathbb{T}^6 \over \mathbb{Z}_2 \times \mathbb{Z}_2}$ orientifold with generalized fluxes and O3/O7-planes. At Step I, we use flux potentials which 1) satisfy tadpole cancellation conditions and 2) have supersymmetric Minkowski vacua with flat direction(s). The 7 moduli are split into heavy and massless Goldstone multiplets. At Step II we add a nilpotent multiplet and uplift the flat direction(s) of the type IIB string theor…
We show that it is possible to combine an early phase of String Gas Cosmology which can explain the origin of the observed structures on cosmological scales with a short later period of power law inflation which creates spatial flatness. The resulting model is consistent with the ``swampland criteria'' and the constraints coming from the {\it Trans-Planckian Censorship Conjecture}. Such a construction is not possible using only canonical slow-roll inflation, but it can emerge in the warm inflation scenario or in cold inflation with an exponential potential. The resulting cosmology is non-singu…
We present an explicit string realisation of a cosmological inflationary scenario we proposed recently within the framework of type IIB flux compactifications in the presence of three magnetised D7-brane stacks. Inflation takes place around a metastable de Sitter vacuum. The inflaton is identified with the volume modulus and has a potential with a very shallow minimum near the maximum. Inflation ends due to the presence of "waterfall" fields that drive the evolution of the Universe from a nearby saddle point towards a global minimum with tuneable vacuum energy describing the present state of o…
We consider models of inflection point inflation. The main drawback of such models is that they suffer from the overshoot problem. Namely the initial condition should be fine tuned to be near the inflection point for the universe to inflate. We show that stringy realizations of inflection point inflation are common and offer a natural resolution to the overshoot problem.
We provide type IIB string embeddings of two axion variants of natural inflation. We use a combination of RR 2 form axions as the inflaton field and have its potential generated by non perturbative effects in the superpotential. Besides giving rise to inflation, the models developed take into account the stabilization of the compact space, both in the KKLT and large volume scenario regimes, an essential condition for any semi-realistic model of string inflation.
We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $Λ$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=λ=0.1$) can be achieved in the case of D-term inflation on the brane.
The observed value of the Higgs mass indicates the possibility that there is no supersymmetry below the Planck scale and that the Higgs can play the role of the inflaton. We examine the general structure of the saddle point inflation in string-inspired theory without supersymmetry. We point out that the string scale is fixed to be around the GUT scale $\sim10^{16}$GeV in order to realize successful inflation. We find that the inflaton can be naturally identified with the Higgs field.
Inflationary scenarios in string theory often involve a large number of light scalar fields, whose presence can enrich the post-inflationary evolution of primordial fluctuations generated during the inflationary epoch. We provide a simple example of such post-inflationary processing within an explicit string-inflationary construction, using a Kahler modulus as the inflaton within the framework of LARGE Volume Type-IIB string flux compactifications. We argue that inflationary models within this broad category often have a selection of scalars that are light enough to be cosmologically relevant,…
Super--inflation driven by dilaton/moduli kinetic energy is naturally realized in compactified string theory. Discussed are selected topics of recent development in string inflationary cosmology: kinematics of super-inflation, graceful exit triggered by quantum back reaction, and clasical and quantum power spectra of density and metric perturbations.
We study a possible origin of the anomalous suppression of the power spectrum at large angular scales in the cosmic microwave background within the framework of explicit string inflationary models where inflation is driven by a closed string modulus parameterizing the size of the extra dimensions. In this class of models the apparent power loss at large scales is caused by the background dynamics which involves a sharp transition from a fast-roll power law phase to a period of Starobinsky-like slow-roll inflation. An interesting feature of this class of string inflationary models is that the n…
This thesis is dedicated to the study of inflationary scenarios based on string theory. Inflation is a brief period of accelerated expansion in the very early Universe which gives natural explanations for problems of the Standard Big Bang Model (SBBM) of cosmology. The phenomenological success of inflation provides the motivation for numerous efforts to establish its connection with particle physics. As a promising contender for a unified theory at very high energy scales, string theory is an obvious framework to look for the theoretical foundations of inflation; we therefore try to determine …
The most important criteria for a successful inflation are to explain the observed temperature anisotropy in the cosmic microwave background radiation, and exiting inflation in a vacuum where it can excite the Standard Model quarks and leptons required for the success of Big Bang Nucleosynthesis. In this paper we provide the first ever closed string model of inflation where the inflaton couplings to hidden sector, moduli sector, and visible sector fields can be computed, showing that inflation can lead to reheating the Standard Model degrees of freedom before the electro-weak scale.
Assuming that the early universe had (i) a description using perturbative string theory and its field theory limit (ii) an epoch of slow-roll inflation within a four-dimensional effective field theory and a hierarchy of scales $M_{inf} < m_{kk} < m_s \lesssim M_{pl}$ that keeps the latter under control, we derive an upper bound on the amplitude of primordial gravitational waves. The bound is very sensitive to mild changes in numerical coefficients and the expansion parameters. For example, allowing couplings and mass-squared hierarchies $\lesssim 0.2$, implies $r \lesssim 0.05$, but asking mor…
In previous works we have derived a Running Vacuum Model (RVM) for a string Universe, which provides an effective description of the evolution of 4-dimensional string-inspired cosmologies from inflation till the present epoch. In the context of this "stringy RVM" version, it is assumed that the early Universe is characterised by purely gravitational degrees of freedom, from the massless gravitational string multiplet, including the antisymmetric tensor field. The latter plays an important role, since its dual gives rise to a `stiff' gravitational-axion "matter", which in turn couples to the gr…
In brane inflation, the relative brane position in the bulk of a brane world is the inflaton. For branes moving in a compact manifold, the approximate translational (or shift) symmetry is necessary to suppress the inflaton mass, which then allows a slow-roll phase for enough inflation. Following recent works, we discuss how inflation may be achieved in superstring theory. Imposing the shift symmetry, we obtain the condition on the superpotential needed for inflation and suggest how this condition may be naturally satisfied.
The lack of power on large scales (l < 40) might have been observed by the PLANCK satellite. We argue that this putative feature can be explained by a phase of fast roll at the onset of inflation. We show that in the context of single field models what is required is an asymmetric inflection point model of which fibre inflation is a string motivated example. We study the ability of fibre inflation to generate a suppression of the CMB 2-point function power at low l, finding that the potential derived from string loops is not steep enough for this purpose. We introduce a steeper contribution to…
Standard D-term inflation is studied in the framework of supergravity. D-term inflation produces cosmic strings, however it can still be compatible with CMB measurements without invoking any new physics. The cosmic strings contribution to the CMB data is not constant, nor dominant, contrary to some previous results. Using current CMB measurements, the free parameters (gauge and superpotential couplings, as well as the Fayet-Iliopoulos term) of D-term inflation are constrained.
In this talk we describe recent progress in construction of inflationary models in the context of string theory with flux compactification and moduli stabilization. We also discuss a possibility to test string theory by cosmological observations.
We examine the consequences of recent developments on Fayet-Iliopoulos (FI) terms for D-term inflationary models. There is currently no known way to couple constant FI terms to supergravity consistently; only field-dependent FI terms are allowed. These are natural in string theory and we argue that the FI term in D3/D7 inflation turns out to be of this type, corresponding to a pseudo-anomalous U(1). T he anomaly is canceled by the Green-Schwarz mechanism in 4 dimensions. Inflation proceeds as usual, except that the scale is set by the GS parameter. Cosmic strings resulting from a pseudo-anomal…
We study symmetry breaking and topological defects in a supersymmetric model with gauge group $\text{U}(2)$, which can be identified with the right-handed part $\text{SU}(2)_R \times \text{U}(1)_{B-L}$ of an extended electroweak symmetry of the Standard Model. The model has two phases of hybrid inflation terminated by tachyonic preheating where either monopoles and strings or, alternatively, dumbbells are formed. In the first case a stochastic gravitational wave background is predicted in the LIGO-Virgo band, possibly extending to the LISA frequency band and to nanohertz frequencies, which is …
Towards the end of the brane inflationary epoch in the brane world, cosmic strings (but not texture, domain walls or monopoles) are copiously produced during brane collision. These cosmic strings are D$p$-branes with $(p-1)$ dimensions compactified. We elaborate on this prediction of the superstring theory description of the brane world. Using the data on the temperature anisotropy in the cosmic microwave background, we estimate the cosmic string tension $μ$ to be around $G μ\simeq 10^{-7}$. This in turn implies that the anisotropy in the cosmic microwave background comes mostly from inflation…
The recent BICEP2 measurements of B-modes indicate a large tensor-to-scalar ratio in inflationary cosmology, which points towards trans-Planckian evolution of the inflaton. We propose possible string-theory realizations thereof. Schemes for natural and axion monodromy inflation are presented in the framework of the type IIB large volume scenario. The inflaton in both cases is given by the universal axion and its potential is generated at subleading order by F-terms. Our models are shown to feature a natural mechanism for inflaton decay into predominantly Standard Model particles.
The predictions for all the cosmological observables of any inflationary model depend on the number of e-foldings which is sensitive to the post-inflationary history of the universe. In string models the generic presence of light moduli leads to a late-time period of matter domination which lowers the required number of e-foldings and, in turn, modifies the exact predictions of any inflationary model. In this paper we compute exactly the shift of the number of e-foldings in Kaehler moduli inflation which is determined by the magnitude of the moduli initial displacement caused by vacuum misalig…
The recent BICEP2 result shows that the Universe once has gone through the vacuum with the GUT scale energy density. The implied high scale inflation nullifies the dilution idea of topological defects, strings and domain walls, of the axionic system. In particular, domain walls are disastrous if the domain wall problem with domain-wall number greater than 1 is present. We argue that the model-independent axion in string compactification with the anomalous U(1) gauge symmetry resolves the domain wall problem naturally with a symmetry principle.
Recent BICEP2 detection of low-multipole B-mode polarization anisotropy in the cosmic microwave background radiation supports the inflationary universe scenario and suggests a large inflaton field range. The latter feature can be achieved with axion fields in the framework of string theory. We present such a helical model which naturally becomes a model with a single cosine potential, and which in turn reduces to the (quadratic) chaotic inflation model in the super-Planckian limit. The slightly smaller tensor/scalar ratio $r$ of models of this type provides a signature of the periodic nature o…
We discuss excitation of string oscillation modes by an initial singularity of inflation. The initial singularity of inflation is known to occur with a finite Hubble parameter, which is generally lower than the string scale, and hence it is not clear that stringy effects become significant around it. With the help of Penrose limit, we find that infinitely heavy oscillation modes get excited when a singularity is strong in the sense of Krolak's classification. We demonstrate that the initial singularities of Starobinsky and hill top inflation, assuming the slow roll inflation to the past infini…
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…
Brane inflation in superstring theory predicts that cosmic strings (but not domain walls or monopoles) are produced towards the end of the inflationary epoch. Here, we discuss the production, the spectrum and the evolution of such cosmic strings, properties that differentiate them from those coming from an abelian Higgs model. As D-branes in extra dimensions, some type of cosmic strings will dissolve rapidly in spacetime, while the stable ones appear with a spectrum of cosmic string tensions. Moreover, the presence of the extra dimensions reduces the interaction rate of the cosmic strings in s…
It is shown that Starobinsky-like potentials can be realized in non-geometric flux compactifications of string theory, where the inflaton involves an axion whose shift symmetry can protect UV-corrections to the scalar potential. For that purpose we evaluate the backreacted, uplifted F-term axion-monodromy potential, which interpolates between a quadratic and a Starobinsky-like form. Limitations due to the requirements of having a controlled approximation of the UV theory and of realizing single-field inflation are discussed.
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 $R_c H=1/2$. On the other hand, larger loops freeze in comoving coordinates, and we explicitly show that they can survive more $e$-foldings of inflation than point-like 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 network…
We discuss how in $SO(10)$ grand unification an observable number density of topologically stable intermediate mass ( $\sim 10^{14}$ GeV) monopoles survive inflation driven by a Coleman-Weinberg potential and non-minimal coupling of the inflaton field to gravity. The scalar spectral index $n_s$ is in excellent agreement with the current observations, and the tensor to scalar ratio $r\gtrsim 0.003$. The model also predicts the presence of intermediate scale topologically stable cosmic strings, and their gravitational wave spectrum reflects the amount of cosmic inflation experienced by the assoc…
Among the inflationary models based on string theory, the D3/D7 model has the advantage that the flatness of the inflaton potential can be protected even with moduli stabilization. However, the Abrikosov-Nielsen-Olesen BPS cosmic strings produced at the end of original D3/D7 inflation lead to an additional contribution to the CMB anisotropy. To make this contribution consistent with the WMAP results one needs an extremely small gauge coupling in the effective D-term inflation model. Such couplings may be difficult to justify in string theory. Here we develop a generalized version of the D3/D7 …
We study the production of dark matter and dark radiation after reheating in string inflation models where the Calabi-Yau has a fibred structure and the visible sector lives on D3 branes. We show how the interplay between different physical constraints from inflation, reheating, supersymmetry breaking and dark radiation, leads to distinct predictions for the nature of dark matter.
Following the 2015 Planck release, we briefly comment on the status and some ongoing opportunities in the interface between inflationary cosmology, string theory, and CMB data. The constraints in the $r$-$n_s$ plane introduce a new parameter into inflationary cosmology relative to the simplest quadratic inflation model, in a direction which fits well with couplings to heavy fields as occurs in string theory. The precision of the data permits further searches for and constraints on additional model-dependent features, such as oscillatory $N$-spectra, a program requiring specific theoretically m…
We investigate the constraints of slow-roll inflation on the string worldsheet. A general gravity-matter set-up is used in which the worldsheet consists of an abstract CFT coupled to a 3+1 dimensional non-linear sigma model. The empirical slow-roll parameters are expressed in terms of the beta functions of operators in the matter/internal CFT and the beta function of the dilaton. The result confirms that inflation is only sensitive to macroscopic properties of the matter sector, and that in string theory inflation is a non-perturbative (in g_s) phenomenon and one must go beyond tree-level stri…
In a simple reanalysis of the KKLMMT scenario, we argue that the slow roll condition in the D3-anti-D3-brane inflationary scenario in superstring theory requires no more than a moderate tuning. The cosmic string tension is very sensitive to the conformal coupling: with less fine-tuning, the cosmic string tension (as well as the ratio of tensor to scalar perturbation mode) increases rapidly and can easily saturate the present observational bound. In a multi-throat brane inflationary scenario, this feature substantially improves the chance of detecting and measuring the properties of the cosmic …
We propose a new type of axion inflation with complex structure moduli in the framework of type IIB superstring theory compactified on Calabi-Yau manifold. The inflaton is identified as the axion for the complex structure moduli whose potential is originating from instantonic corrections appearing through the period vector of mirror Calabi-Yau manifold. The axionic shift symmetry is broken down to the discrete one by the inclusion of instantonic correction and certain three-from fluxes. Our proposed inflation scenario is compatible with Kähler moduli stabilization. We also study a typical rehe…
In this work we study the imprints of a primordial cosmic string on inflationary power spectrum. Cosmic string induces two distinct contributions on curvature perturbations power spectrum. The first type of correction respects the translation invariance while violating isotropy. This generates quadrupolar statistical anisotropy in CMB maps which is constrained by the Planck data. The second contribution breaks both homogeneity and isotropy, generating a dipolar power asymmetry in variance of temperature fluctuations with its amplitude falling on small scales. We show that the strongest constra…
The recent measurements of cosmological parameters by the Planck collaboration favors inflationary models with a redshifted spectrum and a very low tensor-to-scalar ratio. Two well-studied scenarios in the particle physics/string theory literature -- inflection point and Starobinsky inflation -- are in good agreement with these data. In these proceedings, we report on general studies of these two scenarios. We discuss similarities in their structure which, we argue, arise from a common mechanism: degenerate critical point of the potential. In particular, we emphasize their ability to support a…
Within the framework of a novel functional method on the world-sheet of the string, we discuss simple but re-summed (in the Regge slope) inflationary scenarios in the context of closed Bosonic strings, living in four target-space dimensions, in the presence of non-trivial tachyon, dilaton and graviton cosmological backgrounds. The inflationary solutions are argued to guarantee the vanishing of the corresponding Weyl anomaly coefficients in a given world-sheet renormalization scheme, thereby ensuring conformal invariance of the corresponding sigma-model to all orders in the Regge slope. The key…
We propose the natural inflation from the heterotic string theory on "Swiss-Cheese" Calabi-Yau manifold with multiple $U(1)$ magnetic fluxes. Such multiple $U(1)$ magnetic fluxes stabilize the same number of the linear combination of the universal axion and Kähler axions and one of the Kähler axions is identified as the inflaton. This axion decay constant can be determined by the size of one-loop corrections to the gauge kinetic function of the hidden gauge groups, which leads effectively to the trans-Planckian axion decay constant consistent with the WMAP, Planck and/or BICEP2 data. During th…
We study a model of accidental inflation in type IIB string theory where inflation occurs near the inflection point of a small Kähler modulus. A racetrack structure helps to alleviate the known concern that string-loop corrections may spoil Kähler Moduli Inflation unless having a significant suppression via the string coupling or a special brane setup. Also, the hierarchy of gauge group ranks required for the separation between moduli stabilization and inflationary dynamics is relaxed. The relaxation becomes more significant when we use the recently proposed D-term generated racetrack model.
We assess which Kahler potentials in supergravity lead to viable single-field inflationary models that are consistent with Planck. We highlight the role of symmetries, such as shift, Heisenberg and supersymmetry, in these constructions. Also the connections to string theory are pointed out. Finally, we discuss a supergravity model for arbitrary inflationary potentials that is suitable for open string inflation and generalize it to the case of closed string inflation. Our model includes the recently discussed supergravity reformulation of the Starobinsky model of inflation as well as an interes…
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.
After 25 years of its existence, inflationary theory gradually becomes the standard cosmological paradigm. However, we still do not know which of the many versions of inflationary cosmology will be favored by the future observational data. Moreover, it may be quite nontrivial to obtain a natural realization of inflationary theory in the context of the ever changing theory of all fundamental interactions. In this paper I will describe the history and the present status of inflationary cosmology, including recent attempts to implement inflation in the context of string theory.
We describe a scenario for inflation in the framework of non-critical string theory, which does not employ an inflaton field. There is an exponential expansion of the volume of the Universe, induced by enormous entropy production in the early stages of cosmological evolution. This is associated with the loss of information carried by global string modes that cross the particle horizon. It is the same loss of information that induces irreversible time flow when target time is identified with the world-sheet Liouville mode. The resulting scenario for inflation is described by a string analogue o…
We investigate the embedding of brane inflation into stable compactifications of string theory. At first sight a warped compactification geometry seems to produce a naturally flat inflaton potential, evading one well-known difficulty of brane-antibrane scenarios. Careful consideration of the closed string moduli reveals a further obstacle: superpotential stabilization of the compactification volume typically modifies the inflaton potential and renders it too steep for inflation. We discuss the non-generic conditions under which this problem does not arise. We conclude that brane inflation mode…
