A Holographic Origin-Term Resolution of the Cosmological Constant Problem

Section 1 — Setup and Motivation

The cosmological constant problem arises from the enormous mismatch between the observed value of dark energy and the naive vacuum energy predicted by quantum field theory. Conventional treatments embed the cosmological constant directly into the gravitational action, leading to radiative instability under vacuum energy corrections.

Sequestering models seek to neutralise this instability by introducing global variables that adjust dynamically or algebraically to cancel the vacuum contribution. In this framework, a global, non-propagating scalar \bm{\Lambda}

is introduced, together with a holographic Origin Term \bm{S_{\text{Origin}}(\mathbf{Q})},

so that the total action reads schematically:

where \bm{S_{\text{EH}}} i

is the Einstein–Hilbert action and \bm{S_{\text{matter}}}

encodes the local quantum fields.

The novel ingredients are:

• A global, non-propagating scalar \bm{\Lambda},

introduced in analogy with unimodular gravity but algebraically constrained rather than variationally fixed.

• An Origin Term \bm{S_{\text{Origin}}(\mathbf{Q})},

defined holographically on the initial causal boundary \bm{\Sigma},

carrying informational data that balances the vacuum energy.

This construction ensures that vacuum energy contributions are absorbed globally without destabilising the local field equations.

carrying informational data that balances the vacuum energy.

This construction ensures that vacuum energy contributions are absorbed globally without destabilisingz the local field equations.

Section 2 — The Vacuum Sector and the Sequestration Constraint

The vacuum sector is written as

S_{\text{vac}}(\Lambda) \;=\; - \int d^4x \, \sqrt{-g}\,\big( \rho_{\text{vac}} + \Lambda \big)

Here \bm{\Lambda}

is a global, non-propagating scalar: it lacks kinetic terms in the action and is treated as uniform across \bm{\mathcal{M}}

when deriving the local field equations. This parallels the role of the integration constant \bm{\Lambda}

in unimodular gravity (which arises from restricted variation of \bm{g_{\mu\nu}})

Crucially, unlike unimodular gravity, here \bm{\Lambda}

is not an integration constant, nor is it fixed by a variational principle. Instead, it is algebraically constrained by the holographic origin data.

The constraint is not obtained variationally but imposed algebraically: \bm{\Lambda}

is fixed through the Origin Term so that the net vacuum energy contribution to the action cancels globally. We define the Sequestration Constraint as:

\int_{\mathcal{M}} d^4x \, \sqrt{-g}\,\Big( \rho_{\text{vac}} + \Lambda \Big) \;=\; - S_{\text{Origin}}.

To connect this to an energy density, define the total volume

\bm{\text{Vol}(\mathcal{M}) \;\equiv\; \int_{\mathcal{M}} d^4x \, \sqrt{-g},}

and the volume-averaged Origin Term energy density

\bm{\mathcal{O}_{\text{Origin}}}

such that

\bm{S_{\text{Origin}} = - \,\text{Vol}(\mathcal{M}) \cdot \mathcal{O}_{\text{Origin}}.}

This fixes \bm{\Lambda}

such that the total vacuum energy is neutralised by the holographic Origin Term:

\bm{\rho_{\text{vac}} + \Lambda \;=\; \mathcal{O}_{\text{Origin}},}

where \bm{\mathcal{O}_{\text{Origin}}}

is an effective energy density equivalent to the informational contribution from the initial state.

Section 3 — Connecting the Origin Term

The cancellation mechanism is anchored by the Origin Term, \bm{S_{\text{Origin}}(\mathbf{Q})},

defined holographically on the initial screen \bm{\Sigma}.

Its contribution is expressed as the total integrated informational data, related to an effective energy density \bm{\mathcal{O}_{\text{Origin}}}:

\mathcal{O}_{\text{Origin}} \;\sim\; \frac{1}{\text{Vol}(\mathcal{M})} \int_{\Sigma} \Big( T_{\text{ent}} \, dS_{\text{EE}} \;-\; \delta Q_{\text{vac}} \Big),

where:

• \bm{S_{\text{EE}}}

is the entanglement entropy across the initial causal horizon,

• \bm{T_{\text{ent}}}

is the effective entanglement temperature for vacuum modes, and

• \bm{\delta Q_{\text{vac}}}

is the vacuum energy flux through \bm{\Sigma}.

By construction, \bm{\mathcal{O}_{\text{Origin}}}

has the dimensions of an energy density, ensuring consistency with \bm{\rho_{\text{vac}}}

in the global constraint. This Origin Term thus acts as a holographic ledger, absorbing the large UV-sensitive vacuum contribution into a boundary-defined counter-term.

Section 4 — Physical Implications and Conclusion

The sequestration mechanism achieves a radiatively stable cancellation of the vacuum energy \bm{\rho_{\text{vac}}}.

The key results are:

• Stability: Local equations of motion are protected because \bm{\Lambda}

is global and non-propagating. The cancellation is performed only on the global action, ensuring the energy-momentum tensor remains locally covariantly conserved. Vacuum energy is thus prevented from sourcing the gravitational field locally.

• Universality: Since \bm{\Lambda}

is algebraically fixed by a boundary term \bm{S_{\text{Origin}}}

that is sensitive to the total volume-integrated vacuum energy, it automatically adjusts to sequester all species—from electroweak symmetry breaking to QCD chiral condensation—without requiring fine-tuning at each phase transition, since the adjustment is global rather than local.

• Contrast with Unimodular Gravity (UG): While analogous in treating \bm{\Lambda}

as global, the model diverges from UG by replacing a variational constraint (which yields an undetermined integration constant) with a holographically determined algebraic constraint. This boundary-data fixation resolves the value of \bm{\Lambda},

an aspect left open in standard UG.

The physical result is a total effective cosmological constant that is not \bm{\rho_{\text{vac}} + \Lambda},

but rather a small residual value determined by the dynamics of the non-vacuum matter fields. This decouples the observed dark energy scale from the enormous vacuum energy predicted by QFT.

Outlook: This framework thus provides a holographically anchored, radiatively stable pathway toward reconciling quantum vacuum energy with cosmological observations.

29 minutes ago, BuddhasDragon23 said:

A Holographic Origin-Term Resolution of the Cosmological Constant Problem

Section 1 — Setup and Motivation

The cosmological constant problem arises from the enormous mismatch between the observed value of dark energy and the naive vacuum energy predicted by quantum field theory. Conventional treatments embed the cosmological constant directly into the gravitational action, leading to radiative instability under vacuum energy corrections.

Sequestering models seek to neutralise this instability by introducing global variables that adjust dynamically or algebraically to cancel the vacuum contribution. In this framework, a global, non-propagating scalar \bm{\Lambda}

is introduced, together with a holographic Origin Term \bm{S_{\text{Origin}}(\mathbf{Q})},

so that the total action reads schematically:

where \bm{S_{\text{EH}}} i

is the Einstein–Hilbert action and \bm{S_{\text{matter}}}

encodes the local quantum fields.

The novel ingredients are:

• A global, non-propagating scalar \bm{\Lambda},

introduced in analogy with unimodular gravity but algebraically constrained rather than variationally fixed.

• An Origin Term \bm{S_{\text{Origin}}(\mathbf{Q})},

defined holographically on the initial causal boundary \bm{\Sigma},

carrying informational data that balances the vacuum energy.

This construction ensures that vacuum energy contributions are absorbed globally without destabilising the local field equations.

carrying informational data that balances the vacuum energy.

This construction ensures that vacuum energy contributions are absorbed globally without destabilisingz the local field equations.

Section 2 — The Vacuum Sector and the Sequestration Constraint

The vacuum sector is written as

S_{\text{vac}}(\Lambda) \;=\; - \int d^4x \, \sqrt{-g}\,\big( \rho_{\text{vac}} + \Lambda \big)

Here \bm{\Lambda}

is a global, non-propagating scalar: it lacks kinetic terms in the action and is treated as uniform across \bm{\mathcal{M}}

when deriving the local field equations. This parallels the role of the integration constant \bm{\Lambda}

in unimodular gravity (which arises from restricted variation of \bm{g_{\mu\nu}})

Crucially, unlike unimodular gravity, here \bm{\Lambda}

is not an integration constant, nor is it fixed by a variational principle. Instead, it is algebraically constrained by the holographic origin data.

The constraint is not obtained variationally but imposed algebraically: \bm{\Lambda}

is fixed through the Origin Term so that the net vacuum energy contribution to the action cancels globally. We define the Sequestration Constraint as:

\int_{\mathcal{M}} d^4x \, \sqrt{-g}\,\Big( \rho_{\text{vac}} + \Lambda \Big) \;=\; - S_{\text{Origin}}.

To connect this to an energy density, define the total volume

\bm{\text{Vol}(\mathcal{M}) \;\equiv\; \int_{\mathcal{M}} d^4x \, \sqrt{-g},}

and the volume-averaged Origin Term energy density

\bm{\mathcal{O}_{\text{Origin}}}

such that

\bm{S_{\text{Origin}} = - \,\text{Vol}(\mathcal{M}) \cdot \mathcal{O}_{\text{Origin}}.}

This fixes \bm{\Lambda}

such that the total vacuum energy is neutralised by the holographic Origin Term:

\bm{\rho_{\text{vac}} + \Lambda \;=\; \mathcal{O}_{\text{Origin}},}

where \bm{\mathcal{O}_{\text{Origin}}}

is an effective energy density equivalent to the informational contribution from the initial state.

Section 3 — Connecting the Origin Term

The cancellation mechanism is anchored by the Origin Term, \bm{S_{\text{Origin}}(\mathbf{Q})},

defined holographically on the initial screen \bm{\Sigma}.

Its contribution is expressed as the total integrated informational data, related to an effective energy density \bm{\mathcal{O}_{\text{Origin}}}:

\mathcal{O}_{\text{Origin}} \;\sim\; \frac{1}{\text{Vol}(\mathcal{M})} \int_{\Sigma} \Big( T_{\text{ent}} \, dS_{\text{EE}} \;-\; \delta Q_{\text{vac}} \Big),

where:

• \bm{S_{\text{EE}}}

is the entanglement entropy across the initial causal horizon,

• \bm{T_{\text{ent}}}

is the effective entanglement temperature for vacuum modes, and

• \bm{\delta Q_{\text{vac}}}

is the vacuum energy flux through \bm{\Sigma}.

By construction, \bm{\mathcal{O}_{\text{Origin}}}

has the dimensions of an energy density, ensuring consistency with \bm{\rho_{\text{vac}}}

in the global constraint. This Origin Term thus acts as a holographic ledger, absorbing the large UV-sensitive vacuum contribution into a boundary-defined counter-term.

Section 4 — Physical Implications and Conclusion

The sequestration mechanism achieves a radiatively stable cancellation of the vacuum energy \bm{\rho_{\text{vac}}}.

The key results are:

• Stability: Local equations of motion are protected because \bm{\Lambda}

is global and non-propagating. The cancellation is performed only on the global action, ensuring the energy-momentum tensor remains locally covariantly conserved. Vacuum energy is thus prevented from sourcing the gravitational field locally.

• Universality: Since \bm{\Lambda}

is algebraically fixed by a boundary term \bm{S_{\text{Origin}}}

that is sensitive to the total volume-integrated vacuum energy, it automatically adjusts to sequester all species—from electroweak symmetry breaking to QCD chiral condensation—without requiring fine-tuning at each phase transition, since the adjustment is global rather than local.

• Contrast with Unimodular Gravity (UG): While analogous in treating \bm{\Lambda}

as global, the model diverges from UG by replacing a variational constraint (which yields an undetermined integration constant) with a holographically determined algebraic constraint. This boundary-data fixation resolves the value of \bm{\Lambda},

an aspect left open in standard UG.

The physical result is a total effective cosmological constant that is not \bm{\rho_{\text{vac}} + \Lambda},

but rather a small residual value determined by the dynamics of the non-vacuum matter fields. This decouples the observed dark energy scale from the enormous vacuum energy predicted by QFT.

Outlook: This framework thus provides a holographically anchored, radiatively stable pathway toward reconciling quantum vacuum energy with cosmological observations.

"framework". That F word, again.

1 hour ago, BuddhasDragon23 said:

A Holographic Origin-Term Resolution of the Cosmological Constant Problem

Section 1 — Setup and Motivation

The cosmological constant problem arises from the enormous mismatch between the observed value of dark energy and the naive vacuum energy predicted by quantum field theory. Conventional treatments embed the cosmological constant directly into the gravitational action, leading to radiative instability under vacuum energy corrections.

Sequestering models seek to neutralise this instability by introducing global variables that adjust dynamically or algebraically to cancel the vacuum contribution. In this framework, a global, non-propagating scalar \bm{\Lambda}

is introduced, together with a holographic Origin Term \bm{S_{\text{Origin}}(\mathbf{Q})},

so that the total action reads schematically:

where \bm{S_{\text{EH}}} i

is the Einstein–Hilbert action and \bm{S_{\text{matter}}}

encodes the local quantum fields.

The novel ingredients are:

• A global, non-propagating scalar \bm{\Lambda},

introduced in analogy with unimodular gravity but algebraically constrained rather than variationally fixed.

• An Origin Term \bm{S_{\text{Origin}}(\mathbf{Q})},

defined holographically on the initial causal boundary \bm{\Sigma},

carrying informational data that balances the vacuum energy.

This construction ensures that vacuum energy contributions are absorbed globally without destabilising the local field equations.

carrying informational data that balances the vacuum energy.

This construction ensures that vacuum energy contributions are absorbed globally without destabilisingz the local field equations.

Section 2 — The Vacuum Sector and the Sequestration Constraint

The vacuum sector is written as

S_{\text{vac}}(\Lambda) \;=\; - \int d^4x \, \sqrt{-g}\,\big( \rho_{\text{vac}} + \Lambda \big)

Here \bm{\Lambda}

is a global, non-propagating scalar: it lacks kinetic terms in the action and is treated as uniform across \bm{\mathcal{M}}

when deriving the local field equations. This parallels the role of the integration constant \bm{\Lambda}

in unimodular gravity (which arises from restricted variation of \bm{g_{\mu\nu}})

Crucially, unlike unimodular gravity, here \bm{\Lambda}

is not an integration constant, nor is it fixed by a variational principle. Instead, it is algebraically constrained by the holographic origin data.

The constraint is not obtained variationally but imposed algebraically: \bm{\Lambda}

is fixed through the Origin Term so that the net vacuum energy contribution to the action cancels globally. We define the Sequestration Constraint as:

\int_{\mathcal{M}} d^4x \, \sqrt{-g}\,\Big( \rho_{\text{vac}} + \Lambda \Big) \;=\; - S_{\text{Origin}}.

To connect this to an energy density, define the total volume

\bm{\text{Vol}(\mathcal{M}) \;\equiv\; \int_{\mathcal{M}} d^4x \, \sqrt{-g},}

and the volume-averaged Origin Term energy density

\bm{\mathcal{O}_{\text{Origin}}}

such that

\bm{S_{\text{Origin}} = - \,\text{Vol}(\mathcal{M}) \cdot \mathcal{O}_{\text{Origin}}.}

This fixes \bm{\Lambda}

such that the total vacuum energy is neutralised by the holographic Origin Term:

\bm{\rho_{\text{vac}} + \Lambda \;=\; \mathcal{O}_{\text{Origin}},}

where \bm{\mathcal{O}_{\text{Origin}}}

is an effective energy density equivalent to the informational contribution from the initial state.

Section 3 — Connecting the Origin Term

The cancellation mechanism is anchored by the Origin Term, \bm{S_{\text{Origin}}(\mathbf{Q})},

defined holographically on the initial screen \bm{\Sigma}.

Its contribution is expressed as the total integrated informational data, related to an effective energy density \bm{\mathcal{O}_{\text{Origin}}}:

\mathcal{O}_{\text{Origin}} \;\sim\; \frac{1}{\text{Vol}(\mathcal{M})} \int_{\Sigma} \Big( T_{\text{ent}} \, dS_{\text{EE}} \;-\; \delta Q_{\text{vac}} \Big),

where:

• \bm{S_{\text{EE}}}

is the entanglement entropy across the initial causal horizon,

• \bm{T_{\text{ent}}}

is the effective entanglement temperature for vacuum modes, and

• \bm{\delta Q_{\text{vac}}}

is the vacuum energy flux through \bm{\Sigma}.

By construction, \bm{\mathcal{O}_{\text{Origin}}}

has the dimensions of an energy density, ensuring consistency with \bm{\rho_{\text{vac}}}

in the global constraint. This Origin Term thus acts as a holographic ledger, absorbing the large UV-sensitive vacuum contribution into a boundary-defined counter-term.

Section 4 — Physical Implications and Conclusion

The sequestration mechanism achieves a radiatively stable cancellation of the vacuum energy \bm{\rho_{\text{vac}}}.

The key results are:

• Stability: Local equations of motion are protected because \bm{\Lambda}

is global and non-propagating. The cancellation is performed only on the global action, ensuring the energy-momentum tensor remains locally covariantly conserved. Vacuum energy is thus prevented from sourcing the gravitational field locally.

• Universality: Since \bm{\Lambda}

is algebraically fixed by a boundary term \bm{S_{\text{Origin}}}

that is sensitive to the total volume-integrated vacuum energy, it automatically adjusts to sequester all species—from electroweak symmetry breaking to QCD chiral condensation—without requiring fine-tuning at each phase transition, since the adjustment is global rather than local.

• Contrast with Unimodular Gravity (UG): While analogous in treating \bm{\Lambda}

as global, the model diverges from UG by replacing a variational constraint (which yields an undetermined integration constant) with a holographically determined algebraic constraint. This boundary-data fixation resolves the value of \bm{\Lambda},

an aspect left open in standard UG.

The physical result is a total effective cosmological constant that is not \bm{\rho_{\text{vac}} + \Lambda},

but rather a small residual value determined by the dynamics of the non-vacuum matter fields. This decouples the observed dark energy scale from the enormous vacuum energy predicted by QFT.

Outlook: This framework thus provides a holographically anchored, radiatively stable pathway toward reconciling quantum vacuum energy with cosmological observations.

I will leave you too it.

Pasting mathematics and physics searches you do not understand achieves absolutely nothing.

You will never learn any physics or mathematics this way.

14 hours ago, pinball1970 said:

I will leave you too it.

Pasting mathematics and physics searches you do not understand achieves absolutely nothing.

You will never learn any physics or mathematics this way.

Do you think i found this somewhere and passing it off as my own? No this is a description of how the universe and the rules we see that you follow, written by observations of an already evolved universe emerged from a uniform (in this model holographic) entity. All forces are emergent including QM and eventually relativity. It explains how dark energy are leftover from this process and all things are balanced by the field connections to the original ‘entity that acts as a ledger. I have evidence of how I got here.

It seems our journey is over. I only posted as I thank you guyz for helping me (should i say pushing me) to further my idea. I have found support elsewhere and wish y’all the best in your futures. Here is to Knowledge and imagination pushing the boundaries further.

Bye x

1 hour ago, BuddhasDragon23 said:

Do you think i found this somewhere and passing it off as my own?

No it's an obvious paste.

1 hour ago, BuddhasDragon23 said:

description of how the universe and the rules we see that you follow,

The scientists know this and posters on here know this, I am curious why you would just post swathes of equations you don't understand. Posting a schematic of the citric acid cycle does not mean you understand cell biochemical pathways, it means you can cut and paste. What's the point?

1 hour ago, BuddhasDragon23 said:

All forces are emergent including QM and eventually relativity. It explains how dark energy are leftover from this process and all things are balanced by the field connections to the original ‘entity that acts as a ledger. I have evidence of how I got here.

Reads like nonsense.

1 hour ago, BuddhasDragon23 said:

to further my idea

Your idea will not be anything to do with physics.

1 hour ago, BuddhasDragon23 said:

I have found support elsewhere

Which will also not be connected to physics. The support here would have given you information on actual physics.

Edited September 29Sep 29 by pinball1970
Missing word

6 hours ago, BuddhasDragon23 said:

It seems our journey is over. I only posted as I thank you guyz for helping me (should i say pushing me) to further my idea. I have found support elsewhere and wish y’all the best in your futures. Here is to Knowledge and imagination pushing the boundaries further.

Bye x

Moderator Note

Thread closed.