Theory – I. Inflation and Early Universe

The early universe can serve as an ultimate laboratory of high-energy/small-scale physics, some of which can be far beyond our reach on the Earth. Some high-energy events at early times leave observable imprints in Cosmic Microwave Background (CMB), the most important observation in cosmology. The CMB observation can therefore provide precious information about high-energy physics, e.g., INFLATION possibly around 1015GeV, NEUTRINO DECOUPLING around MeV, etc.


Inflation is an extreme accelerated expansion at very early time. It resets an “old” universe and starts a whole new one.

Inflation 1_inflation cut of Cosmic History 2

During inflation, the size of the universe increases in an exponential way—it increases e60 times or more in an extremely short time—and the densities of various physical quantities go to zero. Thereby inflation resets the universe existing before it (let bygones be bygones). Furthermore, inflation starts a new universe:

  • It generates primordial perturbations from “NOTHING”: Quantum fluctuations of vacuum.
  • It gives appropriate initial conditions: Homogeneous, isotropic and flat background space-time; scale-invariant, gaussian and adiabatic primordial perturbations.


The energy scale of inflation can possibly be as high as 1015GeV (especially if the tensor-to-scalar ratio r is around 0.1), which is far beyond that we can reach on the Earth (currently around TeV). This is probably the highest-energy scale one can probe. This scale is near the Planck scale (1019GeV), the ultimate scale for the interplay between gravity and quantum physics. Hopefully the knowledge of inflation can give hints about fundamental physics of these high energies, such as quantum gravity, string theory, extra dimension.


We consider various (hypothetical) physics and events relevant to inflation and investigate their imprints in CMB. The physics about inflation includes:

  • Models of the inflaton field (phenomenological models).
  • Statistical properties of primordial scalar and tensor perturbations: spectrum and non-gaussiantiy.
  • UV modification of gravity.
  • Trans-Planckian physics.
  • Extra dimension, e.g., the braneworld scenario.
  • Reheating
  • The initial state of the universe before the inflation starts.

The imprints in CMB include:

  • Anisotropies of CMB temperature and polarization: spectra and correlations.
  • Quadrupole anomaly & oscillatory features at low l in the temperature spectrum.



Inflation 2_Planck22Fig1


Neutrinos in the Standard Model of particle physics are light and weakly interact with baryons and leptons through the Weak Interaction. They behave like HOT DARK MATTER, which can freely stream through the universe and thereby interfere with structure formation, e.g., slowing down the growth of density perturbations especially at smaller length scales. Accordingly, the properties of neutrinos, particularly their masses and abundance, play an essential role in structure formation. Accordingly, the observations of cosmic structures (e.g. CMB, galaxy surveys, etc.) can give the information about the neutrino masses and the number of the effective neutrino species (N). Surprisingly the current cosmological bound on the sum of the neutrino masses is even more stringent than that from the particle-physics experiments on the Earth.

A possible value of the neutrino mass is around 103eV. This scale is much smaller than that of the Standard Model of particle physics (around TeV), but is intriguingly similar to the scale of dark energy. Do neutrinos and dark energy suggest a new fundamental scale at low energies? Are they connected? These questions have stimulated further investigations.

The process of the decoupling of neutrinos from the thermal bath (photons, electrons, protons, etc.) determines the abundance of the relic neutrinos, which contributes to N. Neutrino oscillation, a property not yet fully understood, may play a role in the decoupling process and therefore affects N. In addition to the Standard Model neutrinos, some hypothetical neutrinos have been proposed, e.g., STERILE NEUTRINOS that are light and do not participate in the Weak Interaction, and MASSIVE NEUTRINOS that are on the heavy side in the Seesaw Mechanism, as opposite to the other side with the light Standard Model neutrinos. Sterile neutrinos may contribute to N; massive neutrinos may play the role of COLD DARK MATTER. How do neutrino oscillation and sterile neutrinos affect N and leave imprints in CMB and cosmic structures? How does the massive neutrino dark matter behave? That requires further investigations.