The standard LCDM model seems to fail to reconcile the H0 measurements from the early Universe and the late Universe. The "H0 tension" has become an increasingly significant mystery to resolve in recent years. Moreover, the S8 (amplitude of matter density fluctuation) measurements also show discrepancies between the early and late Universe within LCDM, although not as significant as the H0 tension. Are they due to the systematic errors in the observations, or is there new physics behind them? What are the possible theoretical solutions for the H0 and S8 tensions? Can we test them?

Related work:
Early Modified Gravity: the phenomenology of modified gravity before recombination
Acoustic Dark Energy (ADE) model: a simple scalar field solution for the H0 tension
Acoustic Dark Energy with Planck and ACT: test ADE with latest Planck and ACT data
Early Dark Sector and Swampland: a model with string theory motivated Early Dark Energy and Dark matter interaction
Trigger Early Dark Sector: explain the Early Dark Energy coincidence problem with its interaction with dark matter
Dark Energy Tracking Structure Growth model: a phenomenological solution to the S8 tension with late time modification of structure growth at dark energy dominated epoch

The precise nature and origin of dark energy still remains unknown. Beyond the simplest cosmological constant model, the dark energy is dynamical and many such models involve an extension to General Relativity. With the advent of direct detection of gravitational waves by LIGO-VIRGO, the propagation of gravitational waves across cosmological scales has become an excellent probe to investigate various dark energy and gravity theories. Investigation of the propagation under modified gravity framework reveals some interesting phenomena, such as echoes and waveform distortions, that can be used for testing gravity with current gravitational wave data.

Related work:
Gravitational Wave propagation beyond General Relativity: echoes, waveform distortion, apparent luminosity distance change, polarization birefringence
Degeneracies between GR lensing and Modified Gravity: exact/partial degeneracies, correction to methods in the literature

The measurements of Stochastic Gravitational Wave Background (SGWB) provide a new window to probe gravity and other fundamental physics. Because of its lower frequency (nHz) sensitivity, it is complementary to LIGO/VIRGO observations. The recent detections from Pulsar Timing Arrays (PTA) make it an exciting rising field. Moreover, it is also possible to detect SGWB with Astronomy in the near future. What can we learn from these observations? New lessons about the fundamental physics?

Related work:
A test of gravity with Pulsar Timing Arrays: the impact on the angular correlations of PTA observations with a general modified dispersion relation in modified gravity
Probing Parity Violation in the SGWB with Astrometry: a null test on the non-vanishing EB correlation signals, the angular correlations, and detectability