⚛️ general relativity

SNe Ia in Standard and Conformal Cosmological Models

This paper demonstrates the classical equivalence between standard and conformal cosmological models regarding the apparent luminosity of Type Ia supernovae, arguing that previously claimed observational discrepancies arise from misinterpreting how local measurement units and absolute luminosity vary with redshift when transitioning between Einstein and Jordan frames.

Original authors: A. B. Arbuzov, V. Shmidt, A. F. Zakharov

Published 2026-10-07

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CC BY 4.0

Original authors: A. B. Arbuzov, V. Shmidt, A. F. Zakharov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

To understand the story of the universe's expansion, scientists rely on a cosmic ruler: the Type Ia supernova. These stellar explosions are so consistent in their brightness that astronomers treat them as "standard candles," objects of known power that allow us to measure vast distances. By observing how dim these supernovae appear from Earth, researchers can calculate how far away they are and how fast the universe is stretching. For decades, this method suggested that the universe is not just expanding, but accelerating, a discovery that led to the idea of dark energy. However, recent, incredibly precise measurements have created a tension in our understanding of the cosmos. Different methods of measuring the expansion rate are now disagreeing with one another, creating a puzzle that challenges the standard model of cosmology. This disagreement has prompted scientists to look closely at the very foundations of how they interpret these observations, asking whether the tools they use to measure the universe might be shifting in subtle ways.

A new study by physicists at the Joint Institute for Nuclear Research and the Kurchatov Institute in Russia tackles this puzzle by examining the mathematical frameworks used to describe gravity and the cosmos. The researchers focused on two different ways of writing the equations for the universe: the standard approach and a variation known as the conformal model. While these two models look different on paper, the authors argue that they are actually describing the exact same physical reality. The confusion, they show, arises from a misunderstanding of what happens to the units of measurement when switching between these two perspectives. In the standard view, the universe expands, and the light from distant supernovae stretches, making them appear dimmer. In the conformal view, the universe appears static, but the fundamental units of measurement, such as the mass of an electron or the size of an atom, change over time.

The core of the researchers' finding is that in this conformal picture, Type Ia supernovae are not the reliable "standard candles" that astronomers assume them to be. In the standard model, a supernova's true brightness is fixed, so any dimming is purely due to distance and the expansion of space. However, the study demonstrates that in the conformal model, the absolute brightness of a supernova actually changes depending on how far away it is. This is because the local units used to measure that brightness—specifically the Planck mass, which sets the scale for gravity and matter—are not constant in this framework. As the universe evolves, the scale of these units shifts, meaning a supernova that looks dim is not just far away; it is also intrinsically less bright in the local units of that time and place.

When the researchers corrected for this shift in the units of measurement, the apparent difference between the two models vanished. They showed that once the changing brightness of the supernova is accounted for, the predictions of the conformal model match the predictions of the standard model perfectly. The discrepancy that some previous studies claimed to find was not a sign that one model was wrong or that the universe behaves differently in a conformal framework. Instead, it was an artifact of treating the supernova as having a fixed brightness in a system where the ruler itself was changing length. By realizing that the "standard candle" is not actually standard in the conformal picture, the authors restored the equivalence between the two descriptions.

This work does not propose a new theory of the universe or suggest that dark energy does not exist. Rather, it clarifies that the standard cosmological model and the conformal model are two different languages describing the same phenomenon. The study concludes that the universe's accelerated expansion remains a valid interpretation of the data, but it emphasizes that the physical equivalence of these models depends on correctly interpreting how measurement units evolve. The findings suggest that the tension in current cosmological data is not necessarily a failure of the standard model, but a reminder that the tools we use to measure the cosmos must be understood within the specific framework of the theory being applied.

Technical Summary: SNe Ia in Standard and Conformal Cosmological Models

Problem Statement
Recent cosmological data, including Type Ia supernovae (SNe Ia) observations, Cosmic Microwave Background (CMB) measurements, and Baryon Acoustic Oscillations (BAO) from the DESI collaboration, present tensions with the standard $\Lambda$ CDM model. Notably, expansion rates derived from SNe Ia differ significantly ( $\sim 5\sigma$ ) from those derived from Planck CMB data within the standard framework. Additionally, correlations between SNe Ia brightness and host galaxy ages suggest the Universe may be in a decelerated expansion phase rather than an accelerated one.

These discrepancies have prompted scrutiny of alternative models, including the Conformal Cosmological Model (CC). Previous studies (e.g., [14, 15, 26]) claimed observational discrepancies between the Standard Cosmological (SC) model and the CC model regarding the apparent luminosity of SNe Ia. These claims arose from the assumption that SNe Ia remain "standard candles" (objects with constant absolute luminosity) when transitioning between the Einstein frame (standard GR) and the Jordan frame (conformal dilaton gravity). The authors identify a critical gap: the physical interpretation of local measurement units and their dependence on redshift in the conformal picture was not adequately accounted for in prior comparisons.

Methodology
The authors employ a comparative analysis of the apparent luminosity of SNe Ia within two frameworks:

Standard Cosmology (SC): Formulated in the Einstein frame using General Relativity (GR).
Conformal Cosmology (CC): Formulated in the Jordan frame using Conformal Dilaton Gravity, derived via a Weyl transformation of the metric.

The methodology involves:

Frame Transformation: Utilizing the Weyl transformation $g^E_{\mu\nu} = \Omega^2_\psi g^J_{\mu\nu}$ to link the Einstein and Jordan frames, where the conformal factor $\Omega_\psi$ is related to the dilaton field $\psi$ .
Redshift Interpretation: Analyzing the origin of the redshift effect in both frames. In SC, redshift results from the expansion of the Universe (photon frequency change). In CC, the Universe is static, and redshift arises from the dependence of energy levels on the scale factor (change in local units of measurement).
Dimensional Analysis: Expressing observables in terms of the reduced Planck mass of the respective frame ( $m_E$ or $m_J$ ) to determine their conformal weights. The authors utilize the invariant $m^2_\alpha ds^2_\alpha$ to ensure physical distances remain consistent across frames.
Luminosity Calculation: Deriving the apparent luminosity ( $\ell$ ) by accounting for photon flux, time dilation, and the scaling of absolute luminosity ( $L$ ) due to changes in local physical constants (e.g., electron mass, atomic energy levels) in the Jordan frame.

Key Contributions and Results
The paper establishes the classical equivalence between the SC and CC models regarding SNe Ia observations by correcting the treatment of absolute luminosity in the conformal frame.

Reinterpretation of Redshift in CC: The authors demonstrate that in the Jordan frame, the redshift is not merely a kinematic effect but a consequence of varying local units. Specifically, the electron mass in Planck units scales as $m^J_e \propto (1+z)^{-1}$ , leading to atomic energy levels scaling as $E^J_n \propto (1+z)^{-1}$ .
Non-Standard Candle Status in CC: The central finding is that SNe Ia are not standard candles in the conventional sense within the conformal picture. Because the absolute luminosity $L$ depends on dimensional constants (like the Chandrasekhar limit), and these constants scale with the local Planck mass, the absolute luminosity in the Jordan frame acquires a redshift dependence:
$L_J = \frac{L_E}{(1+z)^2}$
Restoration of Equivalence: When calculating the apparent luminosity in the Jordan frame, the authors combine the geometric factors (photon flux and time dilation) with the scaling of the absolute luminosity.
- In SC (Einstein frame): $\ell_E \propto (1+z)^{-4} L_E$ .
- In CC (Jordan frame): The geometric factor yields $(1+z)^{-2}$ , but the absolute luminosity $L_J$ introduces an additional $(1+z)^{-2}$ factor.
- Result: $\ell_J \propto (1+z)^{-4} L_E$ .
The final expression for apparent luminosity is identical in both frames. The previously claimed discrepancies in observational predictions stem from the erroneous assumption that $L$ remains constant ( $L_J = L_E$ ) across the frame transformation.

Significance and Claims
The paper claims that the apparent differences in observational predictions between standard and conformal cosmological models are artifacts of differing interpretations of physical quantities during the transition between Einstein and Jordan frames.

Classical Equivalence: The study demonstrates that the SC and CC models are classically equivalent. The conformal model is not a distinct physical theory offering alternative predictions but rather a different, equivalent interpretation of the same cosmological phenomena.
Resolution of Discrepancies: By correctly accounting for the redshift dependence of absolute luminosity in the conformal picture (due to variations in local measurement units), the "Hubble tension" or discrepancies in SNe Ia luminosity distances previously attributed to the conformal model are resolved.
Methodological Insight: The authors emphasize that analyzing conformal weights via dimensional analysis in the respective Planck units provides a transparent and robust method for comparing observables across frames, avoiding the pitfalls of assuming invariance of dimensional quantities like luminosity.

The authors conclude that the conformal cosmological model represents a valid, equivalent description of the Universe at the classical level, provided that the frame-dependence of local physical units is rigorously applied to all observables.

Technical Summary: SNe Ia in Standard and Conformal Cosmological Models

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