Astrophysical transients as cosmological probes

Advancements in the field of cosmology over the past decades have dramatically increased our knowledge of the origin and evolution of the Universe, with increasing precision on measured cosmological parameters. The best model describing the evolution of our Universe is the Lambda Cold Dark Matter ($Lambda$CDM) model. While this model fits numerous observations, some tensions with respect to it have been highlighted. One of the most intriguing is the Hubble tension: a disagreement of $sim 5 sigma$ between the $H_0$ values measured at early- and late-time Universe. It is yet unclear whether this tension arises from subtle systematic uncertainties, or we are observing interesting new physics. Furthermore, the force behind the accelerated expansion of the Universe, called as Dark energy (DE), remains almost a mystery with little to no understanding about its nature and evolution. This thesis aims at using different types of astrophysical transients as cosmological probes. I work on advancing the standardization techniques of three types of transients currently detectable at different redshift scales -- supernovae Type Ia (SNe Ia, $z lesssim 1.2$), superluminous supernovae (SLSN, $z lesssim 4$), and kilonovae (KNe, $z lesssim 0.1$). I use these transients to estimate the Hubble constant and investigate the possibility to standardise their luminosities. The new methodologies developed here are particularly promising to address the Hubble tension problem and to constrain the DE evolution in the next decade with the advent of new instruments, such as the Vera Rubin Observatory, Roman Space Telescope, and the James Webb Space Telescope. For SNe Ia, I develop an innovative method to calibrate their distance scale based on the surface brightness fluctuations (SBF) distances of their host galaxies. I calibrate SN luminosity using a sample of 24 anchor SNe Ia hosted in galaxies with SBF distance measurements. With a Hubble flow sample of $sim 100$ SNe Ia, I estimate $H_0 = 70.50 pm 2.37 (stat) pm 3.38 (sys)$,si{km.s^{-1}.Mpc^{-1}}. This value sits midway in the range defined by the Hubble tension, and is consistent with early and the late Universe $H_0$ measurements within the errors. This work also examines the dependence of SNe Ia luminosity on its host galaxy properties in a comparative study involving different types of host galaxies. Our results point to possible intrinsic differences among the luminosity of SNe hosted in distinct types of environments. This dependence is particularly interesting for estimating the cosmological parameters, and to unveil the nature and environment of SN Ia explosion, which remains largely unknown. Additionally, I explore the use of SLSNe type I as a cosmological probe for the very high redshift Universe. These sources can be detected in their rest frame ultraviolet (UV) up to $z sim 7$ using optical and infrared telescopes. I evaluate their peak magnitude correlations with the light curve properties in the rest frame UV using a sample of 22 high redshift ($ 1 lesssim z lesssim 3.2$) SLSNe-I observed to date. I find a linear correlation between the UV peak absolute magnitudes and rise time, having an intrinsic scatter ($sigma_{int}$) of 0.29. Interestingly, this correlation is further tightened ($sigma_{int} approx 0.2$) eliminating those SLSNe which show a pre-peak bump. This result hints at the possibility that the ``Bumpy" SLSNe could belong to a different population. I also observe weak correlations between the peak luminosity and color indices of SLSNe light curves. No relationship is found between peak magnitudes in the UV band and the decline rate ($Delta M_{15}$) of the light curves in contrast to what is typically found in optical band. The correlations found here are promising and encourage further exploration into the use of SLSNe as high redshift cosmological probes. Finally, I contribute to the investigation of the use of Kilonovae as distance indicators in the local Universe. KNe enable to make an independent measurement of the $H_0$. I apply techniques similar to SNe Ia standardisation with two different sets of KNe properties; measured quantities (decline rate and color) and inferred ejecta quantities (mass, velocity and composition). Considering the only confirmed kilonova, AT2017gfo, associated with GW170817, I standardize it correlating its luminosity with the measured and the inferred quantities. We evaluate $H_0 = SI[parse-numbers = false, number-math-rm = ensuremath]{109^{+49}_{-35}}{km.s^{-1}.Mpc^{-1}}$ for the measured analysis, and $H_0 = SI[parse-numbers = false, number-math-rm = ensuremath]{85^{+22}_{-17}}{km.s^{-1}.Mpc^{-1}}$ and $H_0 = SI[parse-numbers = false, number-math-rm = ensuremath]{79^{+23}_{-15}}{km.s^{-1}.Mpc^{-1}}$ for the two inferred analyses. While waiting for larger samples, this work provides a proof-of-concept for a valuable method to obtain an independent constraint on $H_0$. In summary, my work gives new methodologies to constrain the cosmological parameters and understand astrophysical systematics using different types of transients. The analysis of multi-filter observations at different redshift scales enable us to evaluate the $H_0$ with a complementary set of astrophysical transients. For SN Ia, I demonstrate the potential of the use of SBF measurements to calibrate SN luminosity relations. My results point to an interesting astrophysical difference among SN Ia in different type of galaxies, which could reduce the $H_0$ tension and give information about the progenitor/environment of SN Ia. For SLSNe and KNe, my work inserts in the pioneering works exploring these sources as possible standard candles, with the former at high redshift to constrain dark energy evolution, and the latter as a new independent local probe for $H_0$. The transients explored here have the potential to probe local to $z gtrsim 10$ Universe, back to first generations of stars and well into the deceleration epoch. This work lays the framework for powerful cosmological tools in the upcoming years when larger data samples and larger distances will be accessible with the advent of new instruments.