The study of inflation in string cosmology is one of the main areas of research in the intersection between string phenomenology and cosmology. In string cosmology, while the details of the physics of inflation are often dependent on the specific model of string theory used, there are some generic observable features and deviations from the standard cosmological model which provide useful cosmological bounds on beyond standard model (BSM) theories. Most notable among these are predictions of the exponential nature of the inflationary potential and the identification of the inflaton with the modulus, with associated effects such as early matter domination and the cosmological modulus problem. Separately, the eta problem renders the study of cosmology in the context of string theory, or any other UV-complete theory, essential to correctly predict and constraint observables.

We consider a universe dominated by a spatially uniform scalar field ${\displaystyle \phi }$ with a potential ${\displaystyle V(\phi )}$. The energy density of such a scalar field can be written as^[1]

${\displaystyle \rho _{\phi }={\frac {1}{2}}{\dot {\phi }}^{2}+V(\phi )}$

and the pressure of the scalar field as

${\displaystyle P_{\phi }={\frac {1}{2}}{\dot {\phi }}^{2}+V(\phi )}$

Substituting these into the Friedmann equations, one obtains

${\displaystyle H^{2}={\frac {1}{3M_{Pl}^{2}}}({\frac {1}{2}}{\dot {\phi }}^{2}+V(\phi ))}$

where ${\displaystyle H}$ is the Hubble constant and ${\displaystyle M_{pl}}$ is the Planck mass. We additionally also have the Klein-Gordon equation in FLRW spacetime:

${\displaystyle {\ddot {\phi }}+3H{\dot {\phi }}+V'(\phi )=0}$

These two equations together determine the evolution of the universe. When ${\displaystyle V}$ is sufficiently flat, the potential energy dominates over the kinetic energy, and the universe is said to be in the slow-roll regime. In the limit ${\displaystyle V'\to 0}$, the scale factor of the universe grows exponentially. On the other hand, when ${\displaystyle V}$ is sufficiently steep, the kinetic energy dominates over the potential energy, and the scale factor grows as ${\displaystyle a(t)\sim t^{\frac {1}{3}}}$. This regime is referred to as kination.^[2]

We also define the slow-roll parameters

${\displaystyle \epsilon =-{\frac {\dot {H}}{H^{2}}}}$

${\displaystyle \eta ={\frac {\dot {\epsilon }}{H\epsilon }}}$

It can be shown that when ${\displaystyle \epsilon <1}$, the potential is sufficiently flat for slow-roll inflation to occur. If ${\displaystyle \eta <1}$, then inflationary conditions can persist for long periods of time and the universe may expand sufficiently to solve the flatness and horizon problems.^[3] The slow-roll parameters have particular observational significance, as the main observable result of inflation, scalar curvature perturbations in the cosmic microwave background, have a power spectrum of

${\displaystyle \Delta ^{2}(k)\propto \left.{\frac {H^{2}}{M_{Pl}^{2}}}\right\vert _{k=aH}\propto \left({\frac {k}{k_{*}}}\right)^{n_{s}-1}}$

where ${\displaystyle k_{*}}$ is some reference scale^[4] and ${\displaystyle n_{s}-1}$ is the scalar spectral index, which can be shown for single scalar field inflation to be

${\displaystyle n_{s}-1=-2\epsilon -\eta }$

Hence, the value of ${\displaystyle \epsilon }$ and ${\displaystyle \eta }$ strongly affect the observed scale dependence of the power spectrum from data such as PLANCK 2018.^[5]

It is generally accepted that inflation takes place at energy scales much lower than that of the Planck scale. However, the physics of inflation turns out to be highly sensitive to corrections in the high-energy limit, which require a well-controlled UV-complete theory up to the Planck scale in order to make meaningful physical statements. Two examples of this sensitivity are presented below.

• Baumann, Daniel (2022). Cosmology (PDF). Cambridge, United Kingdom New York, NY: Cambridge University Press. ISBN 9781108937092. Retrieved 13 May 2026.