February 26, 2025
Dear Mr. Stefan Bernhard Rüster,
Your response continues to misrepresent the core discussion by shifting the focus away from the historical and conceptual evaluation of the cosmological constant (Λ) and instead imposing a redefined interpretation beyond what Einstein himself introduced and later abandoned.
First, regarding your assertion that "Λ represents a scalar curvature of spacetime when considering matter-free spacetime," this definition applies strictly within the framework of General Relativity (GR).
However, the historical context of Λ, as introduced by Einstein in 1917, was to artificially maintain a static universe, not as an inherent scalar curvature term to explain cosmic expansion. As outlined in my discussion post, Einstein abandoned Λ following Hubble’s discovery of an expanding universe, considering it his "greatest blunder." Therefore, your insistence on redefining Λ in a broader scope beyond its original purpose and subsequent rejection does not engage with the historical and scientific reassessment presented in this discussion.
Second, you reference Chernin’s work and claim that his modified Newtonian gravitational theory aligns with your position. However, as I previously stated, Chernin et al. explicitly utilized a force-based Newtonian framework to analyse dark energy effects in galaxy clusters without relying on curved spacetime. Your selective emphasis on Eqs. (3) and (4) from https://arxiv.org/pdf/1303.3800 does not negate the fact that Newtonian interpretations of cosmic expansion remain valid and are actively explored independently of GR’s curvature-based approach.
Third, your demand that ECM must demonstrate the perihelion shift of Mercury and light deflection at the Sun is an attempt to dismiss its broader relevance by imposing GR’s validation criteria. This rhetorical approach assumes that ECM should be evaluated solely on terms dictated by GR rather than recognizing its independent explanatory power regarding photon dynamics, dark energy, and effective mass principles. While ECM does provide alternative perspectives on gravitational phenomena, its applicability should not be dismissed based on selectively imposed tests that prioritize GR’s assumptions.
The core intent of this discussion post remains the historical and conceptual reassessment of Λ, its original purpose, and the fair attribution of credit regarding cosmic expansion. Instead of addressing these key points, you have shifted the discussion towards promoting a specific viewpoint that extends beyond Einstein’s own interpretation and subsequent rejection of Λ.
Therefore, I encourage you to either engage directly with the discussion’s outlined premises—namely, the historical use and later abandonment of Λ, its force-based implications versus a curvature-based interpretation, and the fair recognition of contributions by Friedmann, Lemaître, and Hubble—or acknowledge that this discussion does not serve as a platform to uncritically impose an interpretation of Λ that Einstein himself discarded.
Best regards,
Soumendra Nath Thakur
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