Inflation in a Cyclic Universe: The Recurring Birth of Structure ✦
Inflationary cosmology accounts for the uniformity and large-scale structure of the universe via a brief epoch of accelerated expansion. Cyclic models describe repeated phases of contraction and expansion, generating primordial perturbations through alternative mechanisms and removing the initial singularity. Typically these paradigms are contrasted. This work demonstrates their compatibility in a scenario with two scalar fields: one governs the cyclic evolution, the other triggers inflation after each cosmological bounce. Thus, inflation may not be a singular event, but a recurring signature of a cyclic universe.
Context
The standard Big Bang model faces puzzles: the extreme homogeneity and flatness of the universe, and the origin of primordial fluctuations from which galaxies grew. The inflationary paradigm proposed by Alan Guth solves these problems through a brief epoch of accelerated expansion, but leaves questions about what came before. However, theorems by Roger Penrose and Stephen Hawking point to the inevitability of an initial singularity. Cyclic models, inspired by Penrose's conformal cosmology, propose an endless succession of cosmic cycles, yet face their own difficulties, such as accumulation of entropy and the need for quantum-gravity effects for the bounce. Could it be that these two scenarios do not exclude but rather complement each other?
Methods
The authors build a two-field model with an action that includes kinetic interaction between scalar fields φ and ϕ and a potential depending on both fields. The ϕ field governs cyclic expansion-contraction, while φ is responsible for inflation after the transition from contraction to expansion. The Friedmann and scalar field equations are derived from varying the action in a flat universe metric. The key effect is a dissipative term with the Hubble parameter, which, during positive expansion, slows the φ field, putting it into slow-roll regime and triggering accelerated expansion.
Results
The model reproduces predictions close to standard inflationary scenarios. In particular, the scalar spectral index takes the form n_s ≈ 1 – 2/N_CMB, where N_CMB ~ 50–60 is the number of e-foldings between mode horizon exit and the end of inflation. This value matches satellite data on the cosmic microwave background (e.g., Planck) with good accuracy. Moreover, in this picture inflation is not a unique event but arises after each cycle if the φ field is sufficiently far from the potential minimum. Thus, the large-scale structure of our universe may be a legacy of many previous epochs.
Implications
Merging cyclic and inflationary cosmology removes the need to choose between competing paradigms. Inflation becomes a natural phase emerging from cyclic dynamics, not an ad hoc add-on. This changes our view of the origin of dark energy and spacetime structure: if the cycles are infinite, then the conditions for inflation can repeat infinitely. Furthermore, the model opens a path to explaining subtle features of the CMB through field interactions.
Future development
Further development will require exploring the full parameter space of the two-field potential and kinetic interaction. It is important to understand how general the condition for inflation after a bounce is, and whether quantum corrections from scalar fields can affect the stability of cycles. Nonlinear perturbations and non-gaussianities also need to be studied, as they could become observable signatures of cyclic prehistory.
Impact
The work impacts early-universe theory by linking gravitational dynamics of cycles with inflationary expansion. The results are important for interpreting data from cosmological missions and for searching for imprints of previous cycles in the CMB.
Next steps
First, it is essential to calculate perturbation spectra in detail, accounting for trajectory turns in field space and assessing the contribution of entropy modes. It is also important to study connections with quantum gravity models, such as loop quantum cosmology, for a consistent description of the bounce.
Key open problems
The scenario directly addresses unsolved problems: the Big Bang singularity (theorems by Stephen Hawking and Penrose), the nature of initial conditions for inflation, and entropy growth in an eternal universe. The key question—transfer of information from cycle to cycle—remains open, but the proposed formalism can help search for observable traces.
🎯 If inflation truly repeats, the observed homogeneity of our universe might be an echo of inflationary phases in countless previous cycles, and gravitational waves from those epochs may have left a faint imprint in the polarization of the cosmic microwave background.
🎬 The idea of a cyclic cosmos with repeating epochs of creation is reflected in science fiction, for example, in the novel 'World Without End' by Poul Anderson, where characters experience the contraction of the universe and a new Big Bang.
Key numbers
- number of inflationary e-foldings: 50–60 (for modes corresponding to the CMB)
- temperature of cosmic microwave background: 2.725 K
- age of the universe: 13.8 billion years
- fraction of dark energy in the present universe: about 68%
- scalar spectral index: n_s ≈ 0.965 (from Planck data)