This is a fascinating and complex topic, touching on the core tenets of Christianity, historical variations, potential Eastern influences, and alternative theories. Let's break it down:

Mainstream Christian Thought on Death and Afterlife:

• Death as a Transition: Mainstream Christianity views death as the end of earthly life and a transition to an eternal state. This state is determined by one's relationship with God, primarily through faith in Jesus Christ.
• Resurrection of the Dead: A central tenet is the future resurrection of the dead, where believers will receive glorified, imperishable bodies to live eternally with God in a new heaven and a new earth. This is often associated with the second coming of Christ.
• Heaven and Hell: Traditionally, Christian theology describes two primary eternal destinations: heaven, a state of perfect communion with God, and hell, a state of eternal separation from God and punishment for unrepented sin.
• No Rebirth/Reincarnation: Mainstream Christianity generally does not subscribe to the doctrine of rebirth or reincarnation, where the soul transmigrates to new physical bodies after death. Life is seen as a singular opportunity to accept God's grace and secure eternal salvation.

Origen (3rd Century Scholar):

• Origen of Alexandria was a highly influential early Christian theologian and scholar. His views on the afterlife were somewhat nuanced and, at times, controversial compared to later mainstream doctrines.
• Apokatastasis (Restoration of All Things): Origen famously proposed the concept of apokatastasis, the eventual restoration of all created beings to God's perfect state. This included the possibility of the salvation of even the devil and demons after a period of purification.
• Soul's Pre-existence: Origen also speculated on the pre-existence of souls before their earthly embodiment, drawing on Platonic philosophical ideas. This concept, while not directly equating to reincarnation in the Eastern sense, suggested a life of the soul before its current existence.
• Purgatory-like State: Some interpretations of Origen's writings suggest a temporary state of purification after death for those not fully righteous, which could be seen as a precursor to the later Catholic doctrine of Purgatory.
• Condemnation: While influential, some of Origen's more speculative ideas, particularly the pre-existence of souls and the universal restoration, were eventually condemned by later church councils as heretical.

The Cathars of Southern France (12th Century):

• The Cathars were a dualistic Christian sect that flourished in Southern France during the 12th and 13th centuries. Their beliefs differed significantly from mainstream Catholicism.
• Dualism: Catharism posited a fundamental conflict between a good, spiritual God and an evil, material creator god. They viewed the physical world, including the human body, as inherently evil.
• Reincarnation: The Cathars did believe in the transmigration of souls (reincarnation). They saw the soul as trapped in the cycle of earthly existence, moving from one physical body to another until it could achieve spiritual purity and liberation from the material realm.
• Liberation through Asceticism: They emphasized a strict ascetic lifestyle, particularly for their spiritual elite ("Perfects"), as a means to purify the soul and escape the cycle of rebirth.
• Suppression: The Cathar movement was brutally suppressed by the Catholic Church through the Albigensian Crusade.

Branching Out in India:

• There is no historical evidence of mainstream Christian doctrines of death and afterlife "branching out" and evolving into a belief in reincarnation within India through established Christian communities.
• Christianity in India, with its long history dating back to the early centuries CE (e.g., the St. Thomas Christians), has generally maintained its core beliefs regarding death, resurrection, and eternal life, distinct from the Indian concepts of rebirth.
• Any overlap or influence would likely be at an individual or syncretic level, where individuals might blend Christian and Eastern beliefs, but this doesn't represent a formal branching of Christian doctrine within India.

The Book "Jesus Lived in India" and Jesus Preaching Rebirth:

• The book "Jesus Lived in India" by Holger Kersten, along with other similar theories, proposes that Jesus survived the crucifixion and traveled to India, where he lived and taught. These theories often draw on purported historical accounts, similarities between some Christian and Eastern teachings, and interpretations of certain biblical passages.
• Rebirth in these Theories: Some proponents of these theories suggest that during his time in India, Jesus encountered and incorporated the doctrine of rebirth into his teachings. They might point to specific sayings attributed to Jesus as having undertones of reincarnation or the cyclical nature of life.
• Lack of Mainstream Acceptance: It is crucial to understand that these theories are not accepted by mainstream Christian scholarship or theology. There is no widely recognized historical or textual evidence within the canonical Bible to support the idea that Jesus preached the doctrine of rebirth.
• Interpretations: The interpretations of Jesus' sayings to suggest reincarnation are often based on selective readings and alternative translations that differ significantly from mainstream biblical scholarship.

In Conclusion:

Mainstream Christian thought firmly centers on a single life followed by an eternal destiny determined by faith in Jesus Christ and the future resurrection. While historical figures like Origen held some nuanced views on the afterlife, and groups like the Cathars embraced reincarnation, these are not representative of core Christian doctrine. The idea that Christianity branched out in India to incorporate rebirth or that Jesus himself preached this doctrine, as suggested by theories like those in "Jesus Lived in India," lacks historical and textual support within mainstream Christian scholarship. These alternative perspectives often involve reinterpretations and draw on sources outside the established Christian tradition.